Gartside backs Harry for England boss
With Euro 2012 little more than a month away, England are still without a full-time coach after Capello quit in February but Redknapp, whose Tottenham Hotspur side are battling to finish in the Premier League top four, is seen as the favourite.
"I think Harry Redknapp would make a good England coach," FA board member Phil Gartside, who is chairman of Bolton Wanderers, told the BBC.
"He's had success at every club he has been at and he sets teams up to win."
The FA has been guarded about discussing potential candidates and Gartside's comments are the first from within the national association directly backing Redknapp.
"Harry is an outstanding English manager," Gartside added.
"The one quality which I believe the England manager should have is a winning mentality.
"For too long, we have not had a team which is capable of winning a tournament. The most important job for any England manager is to win a tournament for us."
Under-21 coach Stuart Pearce is currently acting as caretaker manager for the senior squad who next face a friendly against Norway in Oslo on May 26.