The Burnley midfielder claims McClaren tried bringing him back to St. James' Park.
Barton, who spent four years at St. James' Park, claimed that both he and then head coach Steve McClaren were keen on the move, which was subsequently vetoed from above.
He told Talksport: "Steve wanted to sign me at Derby because he knew I was out of contract at QPR. 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 was part of Newcastle's team the last time they were relegated from the Premier League, but emerged as a key player as the club returned to the top flight the following campaign.
Despite this, the 33-year-old claimed that he and others were soon forced out of St. James' Park, having stood up to then managing director Derek Llambias.
And, according to Barton, his understanding of the club could have proved vital in the Magpies' latest quest to survive the drop, which ended unsuccessfully.
He added: "I’d communicated to Steve, if you don’t get someone like me in there... I knew what they had, I knew they were in trouble. 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."
Barton later signed for Burnley instead, and was an ever-present as Sean Dyche's men ended their first season back in the second tier as champions.
The Liverpudlian was subsequently named in the PFA's divisional team of the year for his efforts.