The 30-year-old Argentinian midfielder effectively took his leave of the Magpies over the weekend when he posted a series of messages on Twitter, and Press Association Sport understands his future may be resolved within the next 24 hours.
Gutierrez tweeted: "It was an honour and a pleasure to play with the Newcastle shirt and to have the support of the Geordie."
After receiving a deluge of replies, he added: "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."
Gutierrez joined Newcastle from Real Mallorca during the summer of 2008, when he signed a five-year contract.
He has made 195 appearances for the club and scored 11 goals, although he has figured only twice this season, starting the 4-0 defeat by Manchester City on the opening weekend of the campaign and then coming on as a substitute in the 2-1 Barclays Premier League victory at Cardiff on October 5.
Gutierrez was a key player for Hughton, who was in charge at St James' Park between June 2009 and December 2010, as he led the Magpies out of the Championship and back into the top flight.