The Sun says Nolan still had two years left on his £40,000-a-week Toon contract but talks over a new deal had broken down after months of negotiating.
Newcastle offered him a £500,000 bonus if the club finished 10th or above next season, plus an extra 12 months on his contract with a £10,000-a-week pay rise. But Nolan, 28, wanted a five-year deal and talks collapsed.
A Toon insider said: "Kevin was a big part of the club and the feeling is that he has done a great job for Newcastle in his time.
"But the offer made to him was seen as extremely generous to reflect that. The fact that a final agreement couldn't be reached is a shame and the fans will be hurt but the powers that be are thinking of the best terms for the club as a whole."