The former England and Arsenal player said that the BBC's football coverage was too formal, and objected to its jackets and ties dress code.
He told Broadcast magazine: "Times are changing. I don't know how long young
people are going to want to sit down and watch that same old 'jacket and tie' format.
"Fans want people who are dressed like them. They've got no one to relate to on TV and that's why I've said I don't want to do the England games any more."
Wright also claimed that he was merely expected to be a "comedy jester" to break the ice with Alan Shearer and Alan Hansen, who "just do run of the mill things".
The BBC denied that he was required to play a jester role and said that he was hired as a retired international player to give his own "expert opinions in his own style".
If Wright stayed at the BBC, there would probably be little work in any case, due to the BBC's loss of international matches and the FA Cup to ITV from August.
Wright will continue with his afternoon programme on TalkSport radio and will host the revived series of 'Gladiators' with Kirsty Gallacher on Sky One in the summer.
He joined the BBC in 2001 and has fronted shows including 'I'd Do Anything', 'Friends Like These' and 'The National Lottery Show'.