Incoming Fifa vice-president Jim Boyce has told the BBC that he believes new FA chairman David Bernstein can help repair relations between the bodies.
Boyce, who replaces Geoff Thompson on Fifa's executive committee next year, says Bernstein's diplomacy will be key after the 2018 World Cup vote debacle.
"England are a major force in world football and relationships with Fifa should be at a high level," he said.
"I'm sure Mr Bernstein will try to ensure that relationships do improve."
Arsenal manager Arsene Wenger has expressed his shock at the decision to overlook former Gunners vice-chairman David Dein for the role.
Mr Bernstein says he is a diplomat and diplomatic relations are important
Dein played a key role in bringing Wenger to the club and worked alongside him until 2007 when he stepped down and Wenger believes his former colleague would have been the ideal choice to take the FA forward.
"I was completely surprised and disappointed [by the FA's decision]," said Wenger.
"He would have offered a competent knowledge of football and international football. It is a disappointment."
England's failure to land the 2018 World Cup, garnering just two votes, led to much criticism of Fifa and its voting processing by England bid representatives, with bid chief executive Andy Anson calling on the world's major football associations to come together and put Fifa under pressure to reform.
But Irishman Boyce is confident the former Manchester City chairman, who sits on the boards of several companies including French Connection, Ted Baker and Blacks Leisure, can bring stability to the FA and improve England's standing within Fifa.
"Mr Bernstein says he is a diplomat and diplomatic relations are important," added Boyce.
"There has been a lot said and written but at the end of the day Fifa are still the governing body of football and England are a member of Fifa and I hope that trust can be rebuilt.
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"I think he has got to be open and honest and I hope that the people that he meets at Fifa will be equally so, and I'm quite certain they will be.
"There have been too many changes for one reason or another at the FA over the last few years with various chairmen and chief executives.
"That is part of life but hopefully now they have the stability they need and I'm certain Mr Bernstein will do everything in his power to ensure that English football goes to the forefront where it should be."
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