The Chronicle claims that the Toon right-back is happy to stay on Tyneside despite interest from Aston Villa, Queens Park Rangers and Fulham.
Simpson snubbed a new deal back in January which was thought to run for four-and-a-half years.
The Chronicle: A source close to Simpson said today: “Danny loves it in Newcastle and is excited about next season.
“He wants to stay at Newcastle next year and then see what happens.”
However, the 25-year-old defender is now heading into the final season of his current contract with his long-term future uncertain.
Yet Simpson is keen to be a part of it at Newcastle at least until the end of next season. He said recently: “It would be massive for me to part of a Newcastle team playing in Europe.”