The long-serving winger has suggested on social networking site Twitter that he is set to leave the club.
Gutierrez, under contract at St James’s Park for another 18 months, has made just two appearances for the club this season, and there has been rumour of a rift between him and Alan Pardew.
There has been speculation about his future in recent weeks.
In response to a question from supporter @CabayeGotNews4U, Gutierrez tweeted: “It was an honour and a pleasure to play with the newcastle shirt and to have the support of the Geordie.”
And the 30-year-old made a second post wishing his team-mates good luck in response to messages from fans.
Gutierrez tweeted: “thanks for the messages. I enjoy my 5 years at the club, I hope the club finish the highest this season and the best to my team mates.”
He has not featured for the first team since returning from a spell of “personal leave” in his native Argentina earlier in the season.
Gutierrez has made 195 appearances, and scored 11 goals, for Newcastle since joining from Real Mallorca in the summer of 2008.