Campbell, 39, who was born in east London to Jamaican parents, claimed the FA decided it could not have a black face leading the England side on a regular basis.
"It's crazy," he was quoted as saying in extracts from biography. "I don't think it will change because they don't want it to, and probably the majority of fans don't want it either."
"It's alright to have black captains and mixed race in the Under-18s and Under-21s but not for the full national side."
The FA has declined to comment on the claims.
Former Tottenham Hotspur and Arsenal defender Campbell, who has 73 caps, captained England under Glenn Hoddle against Belgium in 1998 aged 23 years and 248 days when he became their second youngest skipper after World Cup-winner Bobby Moore.
He was given the armband again by Hoddle against the Czech Republic, also in 1998, and led his country out against the United States in 2005 when Sven-Goran Eriksson was manager.
Campbell played at three World Cups, featuring in 10 games and scoring once, plus three European Championships before announcing his retirement in 2012, having been released by Newcastle United the previous year.
"I think the FA wished I was white," added Campbell. "I had the credibility, performance-wise, to be captain... and I was a club captain early on in my career (at Spurs). I believe if I was white, I would've been England captain for over 10 years."
Campbell also said he did not understand why former Liverpool striker Michael Owen was made captain ahead of him.
"The more caps I won, the further away I seemed to be pushed from becoming captain," said Campbell, who won two Premier League titles and three FA Cups with Arsenal, a League Cup with Tottenham and another FA Cup with Portsmouth.
"I played well, acted honourably on and off the field, but there was little recognition. Owen was a fantastic forward but nowhere near being a captain. It was embarrassing. I kept asking myself: 'what have I done?'
"I've asked myself many times why I wasn't (made captain). I keep coming up with the same answer. It was the colour of my skin."
In an interview with The Sunday Times magazine, Campbell said the soccer hierarchy needed to "change its mentality" and "get more people from other backgrounds, black and Indian, and get them involved in the leadership of the game.
"A lot of black players are now playing for England and if you want to represent that properly you've got to change the backroom staff to have a bit more colour in there."
- Sports & Recreation
- Glenn Hoddle
- Tottenham Hotspur