Tottenham and West Ham both made final submissions on Friday in their bids to take over the venue in east London.
The Premier League football clubs have already handed in detailed proposals to the Olympic Park Legacy Company (OPLC).
In an open letter, Pele gave support to Spurs’s plan to remove the athletics track if their bid is successful.
And Greaves, who scored 220 goals in 321 games for Spurs, said he sympathised with fans who are against moving from current home White Hart Lane but that “reality has got to take a grip”.
Brazilian legend Pele said: “I understand they are based on creating a dedicated football stadium and providing an athletics legacy at the original home of athletics (as I remember it!) Crystal Palace,” he said.
“That would be a great stadium. I really don’t understand wanting to play with a track around the pitch. The players won’t like it and it probably won’t last.
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“As a player I need to feel the passion and the intensity of the fans. The best stadiums connect the fans to the pitch and if you lose that you lose something that really matters and eventually you lose the fans.”
Greaves, who also played a season for West Ham, told BBC Sport’s Dan Roan: “I’m for [the move to Stratford]. The opportunity for a new, modern stadium with decent transport links is a must.
“I know I’m upsetting a lot of Spurs fans but most don’t even live in the area so I don’t see the problem.”
Greaves added that he would also not have a problem with Spurs and West Ham sharing the ground, as was the case when he played for AC Milan in the San Siro.
He said: “I’ve always questioned why the two clubs don’t get involved. It should be a consideration, although I accept it won’t happen in this case.”
The supplementary information included in the final submissions will be used by OPLC chief Andrew Altman to make a recommendation to his board ahead of a meeting on 28 January.
While Tottenham plan to remove the athletics track if their bid is successful, West Ham have vowed to keep it.
Both clubs’ plans have come in for criticism with the head of world athletics Lamine Diack – who is also a member of the International Olympic Committee – telling BBC Sport that London will have told a “big lie” to get the Olympics if the main stadium were to lose its track.
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He added: “While concerns have been raised about sightlines for football we should recall that football has often shared with other sports.
“The old Wembley Stadium had a track around the pitch which was not only used for athletics but for speedway and greyhound racing.”
Three out of the last four Champions League finals have been held in Olympic Stadiums which have athletics tracks surrounding the pitch.
Part of Tottenham’s plan involves the redevelopment of the athletics facility at Crystal Palace’s National Sports Centre (NSC), leading Spurs non-executive director Sir Keith Mills to stress on BBC Radio Four’s Today programme on Friday that their bid would therefore not leave London after 2012 without an athletics track.
Mills, who is also deputy chairman of the London Organising Committee for the Olympic Games (Locog), said: “Lamine Diack quite rightly wants to see the Olympic legacy left in London and both of the bids on the table provide an athletics legacy.
“The issue here, and the one the OPLC will be looking at in the next 10 days, is what’s going to provide the best long-term legacy for London and for the country. And that’s all about which of the two bids is going to be economically viable in the long term.
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“Someone has to pay for the next several decades for the stadium, and if West Ham have found a way to work that economically, the OPLC will look on that favourably. But I find that difficult to see.”
Meanwhile, Crystal Palace Football Club unveiled plans earlier this week to move from Selhurst Park back to their original home at the NSC, a decision that could have an impact on Spurs’ plans.
Tottenham have been given planning permission to redevelop White Hart Lane but chairman Daniel Levy said on Friday he had “concerns about the viability and deliverability” of the proposed update of White Hart Lane.
He added: “The cost of consent has been high. No progress has been made with the remaining land owners and this is a potentially costly issue.
“Compulsory Purchase Orders are of course one route to resolving this, but that process is uncertain and can take years to conclude.”
Former British Olympic Association chairman Sir Craig Reedie and UK Athletics head coach Charles van Commenee have condemned Spurs’ proposal to remove the running track, although former Tottenham chairman Lord Sugar says their plans for the Olympic Stadium and Crystal Palace make perfect sense.
West Ham’s plan to retain the running track, has been described as “madness” and unworkable by former British Olympic Association chief executive Simon Clegg.
And Tottenham manager Harry Redknapp believes West Ham’s path could lead to the venue becoming a “desolate graveyard”.
Redknapp, who also managed the Hammers, from 1994-2001, wrote in his column in the Sun newspaper: “Try to mix football and athletics and you end up with a great big bowl of nothing.
“What if West Ham are relegated this season and then find themselves in a 60,000-capacity stadium in a Championship match?”
West Ham will be loaned £40m by Newham Council to help with their redevelopment plans if they are chosen as preferred tenants of the Olympic Stadium.
And in a statement, the Hammers said: “There are seats at Wembley stadium (regarded as having great views from every vantage point) which are further away from the pitch than any seat in our proposed stadium.
“The club will use state of the art pitch technology aided by excellent air flow to ensure the playing surface is of the highest standard required to compete on a global stage.”
Hammers skipper Scott Parker, giving West Ham’s bid a last-minute boost at a photo opportunity on Friday, said: “I think everything works out perfectly, geography-wise and to move the club forward.
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“It will be exciting, you want to play in the best stadium and the Olympic Stadium will be that.”
The OPLC is expected to decide on its preferred bidder after a board meeting scheduled for Friday, 28 January, although, with the Crystal Palace FC development, a final decision may not be made until the end of the financial year in March.
Its recommendation then has to be ratified by two government departments – the Department for Culture, Media and Sport, and the Department of Communities and Local Government – and the London Mayor’s office.
Former Olympic javelin champion Tessa Sanderson will not be permitted to play any part in the decision due to a conflict of interest, it was revealed on Wednesday.
Sanderson is an OPLC board member but she also has a contract with Hammers’ partner Newham Council.
However, she claimed on Friday there was no conflict of interest and said: “I hope it doesn’t come to it but I am willing to take legal action if necessary.”
