Barton was controversially given a free transfer by the club in the summer of 2011 after criticising the hierarchy on Twitter.
And the midfielder – who helped Burnley win the Championship this season – has revealed that he had conversations with newly-appointed United head coach Steve McClaren about a return at the start of the season, when he was a free agent.
Speaking on talkSport, Barton said: "Steve wanted to sign me at Derby, because he knew I was out of contract at QPR.
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"He obviously lost his job at Derby, and wanted to sign me for Newcastle.
"I spoke to him a few times over the summer, and he was told, basically, the Pope had more chance of playing for Newcastle than me."
Barton, in the United side which won the Championship in 2009-10, has questioned whether the relegated club has the same character in the dressing room.
The 33-year-old said: "You need a core nucleus of people who know what the football club’s about.
"We had that last time, they haven’t got that this time."