The midfielder is entering the final 12 months of his contract at St James' Park after talks over a new deal broke down.
Unless negotiations over an extension resume, Barton could either see out the next year before leaving Tyneside on a free transfer next summer, or leave during the current transfer window if Newcastle decide they want to cash in.
He has been linked with a move to relegated West Ham, where he would be reunited with former team-mate Kevin Nolan and manager Sam Allardyce, who brought Barton to Newcastle in 2007.
However, the 28-year-old maintains that he has no interest in playing for a second-tier club as he wants to test himself against the best in the business.
"Contract negotiations not re-opened. Back to NUFC on Tuesday, Happy days," Barton wrote on Twitter.
He added: "Why would I drop down a league when I can more than hold my own in the Premiership?
"What benefit would it give me? None.
"I play this game to play against the best week in, week out."