The ex-Celtic striker and pundit cited his former manager’s body language and some of the comments made by Strachan over the summer as the reason for his opinion.
The Scotland boss is under pressure after the 1-1 draw with Lithuania on Saturday evening, a result which dented the nation’s hopes of qualifying for World Cup 2018 and finally ended the long wait for an appearance at a major international tournament.
Strachan made headlines last week when he cut down a BBC reporter, who wished to ask questions the “fans wanted answered”.
The 59-year-old also made some curious comments over the summer, questioning the ability of his players prior to a friendly double-header with Italy and France, as well as lamenting the lack of a world class superstar within the Scotland ranks.
Sutton feels all of this is being said by a man whose heart is no longer in it.
He told BBC Radio 5Live: “Gordon Strachan doesn’t want to be there any more as Scotland manager, in my opinion.
“I thought his comments in the summer were appalling. He said Scotland were a scared nation of scared footballers. I think the impact that would have had on the players at that time, they would have been totally disgruntled.
“I think he’s losing credibility with the fans. I don’t agree that a lot of fans are still on his side. Gordon Strachan talks about how Scotland don’t have a Gareth Bale or one of the big stars, but the fans look at Iceland or Northern Ireland and their performance, and think we want a piece of that.
“His attitude towards certain people in the last week, he’s been rude and cantankerous, and I just feel he doesn’t want to be there any more. He’s showing that in every interview with his body language.”