The head of English football said boycotting the World Cup alone would be "ridiculous" but said pressure could be put on other footballing nations for support in the wake of the Fifa corruption row.
It comes after the Duke of Cambridge urged world football's governing body to "show that it can represent the interests of fair play and put the sport first".
Uefa has not ruled out asking European nations to snub the footballing tournament if re-elected Fifa president Sepp Blatter does not step down following the arrest of football officials over decades of "rampant" corruption this week.
But FA chairman Greg Dyke told the BBC's Andrew Marr Show that Britain would not be able to make a stand against Fifa without wider support.
"Putting pressure on Sepp Blatter is pretty impossible," he said.
"But putting pressure on other footballing nations and putting pressure on sponsors is a good idea, I think."
Speaking of a boycott, he added: "It would be ridiculous to try and do it on your own. All we would do is pull out of the World Cup and everyone would say 'well done' and forget all about us.
"It's got to be done by enough nations for it to have an impact, if it's done, but I don't think Blatter will last four years.
"We were without doubt one of the stronger voices this week saying something has got to be done but I don't think there's any point the FA doing it on its own, we've got to do it along with other countries, alongside other large footballing nations."
The proposal of a Fifa World Cup boycott was first threatened by Uefa head Michel Platini, who will meet European footballing nations next week to decide how they take a stand against Mr Blatter.
Culture Secretary John Whittingdale told the Sunday Times that England and Uefa were right to consider turning their backs on the tournament, adding "no options should be
Prince wades into row
The Duke, who is president of the Football Association (FA), urged sponsors and other backers to press for reform after a week which saw seven Fifa officials arrested and 18 people connected to football indicted on corruption charges by the US justice department.
He used his speech before the FA Cup final to also back the decision by former Manchester United chief executive and newly elected Fifa vice-president David Gill to quit the position almost immediately in protest at Mr Blatter's re-election as the organisation's president.
Speaking at Wembley before Arsenal's 4-0 victory over Aston Villa, William said: "There seems to be a huge disconnect between the sense of fair play that guides those playing and supporting the game, and the allegations of corruption that have long lingered around the management of the sport internationally.
"Those backing Fifa, such as sponsors and the regional confederations, must do their bit to press these reforms - we are doing football and its fans no favours if we do not.
"I have no doubt that when Fifa reforms, its mission to spread the benefits of the game to more people, especially those in developing countries, can only be enhanced."
William said he "commended" Mr Gill's decision to stand down and said the FA should act as an example to Fifa of good governance, having taken "a critical look at itself under Greg Dyke's leadership".
The Duke added: "Over the next few years, if we want credibly to influence the debate on reform in Fifa, we must continue to strive for excellence in our own organisation.
"It's not easy to do so, but it is worth it - and, to that end, I commend the process you are on, and I'll be watching it closely."
Mr Blatter yesterday criticised Mr Gill for rejecting his position and said he will not forget Uefa's "hate" campaign calling for him to be ousted from his role as leader, an appeal backed by the FA and Prime Minister David Cameron.
He claimed the bid to unseat him was down to "English media and the American movement" because of their failed World Cup bids and the arrest of seven Fifa officials on US corruption indictments in Zurich was a possible attempt to interfere with the congress, where he was re-elected on Friday for a fifth term as president.