Architects in charge of rebuilding Wembley next summer say the towers have to be removed in order to move the stadium north of its current site and thus help accommodate the new facilities, including a running track around the pitch.
The news has been greeted with dismay by many famous players, who feel the towers are synonymous with the stadium's heritage.
However, Sir Stanley, honoured yesterday for his performance in the 1953 FA Cup final, "the Matthews final", believes Wembley will still maintain its status as the home of football - with or without the towers.
"It's a matter of fact that the twin towers have to go," said the 83- year-old. "But to me the most important thing is that Wembley is still Wembley, the position is still there, the stadium is still there. Wembley is about the name. If you played Cup finals in Manchester or Birmingham it wouldn't be the same. You can't describe the atmosphere."
The Football Association's director of public affairs, David Davies, added: "No final decision has been taken, though there will have to be one soon. Everybody wants the finest stadium in the world to be built on this site and everybody knows the emotional attachment of many, many people to the twin towers.
"The question is can we reconcile those two facts and then pay for it and that's what the discussions will centre on."
Sir Stanley, European footballer of the year in 1956, played his final game on 6 February, 1965 at the age of 50, but yesterday revealed he could have carried on his extraordinary career for even longer.
He added: "It was a bad mistake to stop playing. I still had my pace and I think I could have gone on another two years but I thought 50 was a good age."
Matthews played almost 400 games for Blackpool but will always be remembered for his part in their 1953 Cup final triumph, when he inspired their comeback from 3-1 down against Bolton to win 4-3.
At Wembley yesterday he was presented with the first AXA FA Cup Legends Award, and reunited with team-mates Bill Perry and Cyril Robinson.
It was Perry who headed home Matthews' cross for the last-minute winner in 1953, and he paid tribute to his former colleague. "As a player he was so brilliant," Perry said. "You sometimes stood there watching and forgot you had to get in the penalty area."
Brent Council, which runs the district that includes Wembley, said it would reject any planning application that does not safeguard the future of the towers. "They are an important part of our heritage and we will fight to keep them," John Duff, Brent's environment committee chairman, said. "Our planning briefing is to keep the towers and we are not about to change our minds."
English Heritage, the government body which advises on historic buildings, said it was still pushing for a design which would involve shifting the towers rather than pulling them down.
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