Johansson has been president since 1990 and, launching his manifesto for a last four-year spell, said: "I spoke with Chancellor Gordon Brown and he is very keen on the idea of it coming back to England.
"After Germany this year, it is going to South Africa in 2010 and then to South America in 2014.
"The next time it might be back in Europe would be 2018. England have not had the World Cup since 1966 and I know there is a great deal of interest to support such a project."
FIFA move to clear way for England bid
Football Association chairman Brian Barwick confirmed that a bid would be considered.
"If  is the year it is going to come back to Europe, we're going to go for it," he said.
The final decision will not be made until 2012, the year London hosts the Olympic Games. British sports minister Richard Caborn confirmed that the government would back a bid for the finals.
"We would be in very serious contention," he said. "If we have a good 2012 Olympics, it will put us in the premier division of countries for running sports events."
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