The 28-year-old former Manchester City midfielder was linked in the Sunday Times with a possible move to Manchester United, the latest of several clubs to be tipped to bid for Barton.
But Barton, who has one year left on a Newcastle contract which is unlikely to be renewed, looks set to stay at St James' Park.
He wrote on Twitter: "Nice to be linked with some big clubs today but I honestly don't want to leave Newcastle. Thanks but no thanks."
He added: "I will most likely leave Newcastle at end of season, when my contract expires and I am no longer employed. Its [sic] out of my hands."
ARE YOU WATCHING MICHAEL OWEN ... YOU MONEY-GRABBING LITTLE TURD?