Should England beat Sweden and then either Croatia or hosts Russia in the semi-finals the most important game in English soccer since 1966 would almost certainly overlap with the men's singles final at the All England Club on Sunday week.
Wimbledon have said they will not budge from their 1300 GMT start time for the men's final. The World Cup final in Moscow will kickoff at 1500 GMT.
"Absolutely they should bring it forward," Wilander, who is Eurosport's chief analyst during Wimbledon, told Reuters.
"I think Wimbledon would be very smart to do that. I would say that the players would even agree to do that. I do.
"It's a very interesting point. England should get to the final now. I really think they should move to one pm. They want people to watch the Wimbledon final and sponsors would want that too. Everybody would want that.
"The television contracts around the world could be the problem though. But I think they should have considered changing the time before the tournament started. Not because it's England but because it's the World Cup final."
Wimbledon is being played out to a backdrop of World Cup fever with England having reached the last eight.
Saturday's quarter-final which kicks off at 1400 GMT could clash with British player Kyle Edmund's third-round showdown with three-times Wimbledon champion Novak Djokovic.
The sensible option would be to schedule Edmund's match as the last match on a showcourt which would mean England's game would likely be over before he starts.
"I'm sure they'll factor that in," Edmund, who is a big soccer fan, told reporters. "I mean, obviously I'm a tennis player, so I'm here to do my job first.
"But we'll see. I don't know. Hopefully it will be a success for both of us, England and myself."
Like Wilander, Edmunds's coach Freddie Rosengren is a Swede and the pair were photographed wearing their respective country's shirts this week exchanging pretend punches.
"Hopefully we get to watch the match. It's been a bit of fun the way it's worked out, that we play Sweden," Edmund said.
Wilander believes Sweden might upset the odds just like so many unseeded players have done at Wimbledon this week.
"I think it's a good situation for Sweden, I really do," Wilander said. "England are the big favourites and it's a great draw for them, they are the better team, but I'm not sure England can break down the system the Swedes play."
(Reporting by Martyn Herman; editing by Clare Fallon)
