Manchester United and Real Madrid legend Beckham, who will be 37 by the time the Games begin, is widely considered a certainty to be one of the three over-age players in the 18-strong squad that will otherwise consist of Under-23s.
"If you are going to pick the best three over-age players then you would say no [to Beckham]," Lineker told the BBC.
"If it is a 'thank you' for all the work that Beckham has done for the Olympics and getting it to London, then it is a different matter.
"I would pick my best three players if I was in charge. That is who I would want, but who knows? It might be a done deal."