The Argentina international remained with the relegated Magpies over the summer as a host of big-name players moved on from the North East.
Michael Owen, Obafemi Martins, Damien Duff and Sebastian Bassong all sought pastures new as Newcastle dropped down in to the Championship.
And although Gutierrez remained and has been a regular for Chris Hughton's side as they target an immediate return to the top-flight, he could not be set to move on for pastures new.
InterestedHis agent, Pedro Jimenez-Bravo, is quoted by The People as saying: "We know European clubs are interested.
"We have held meetings with Newcastle but there is an option for the player to leave - although it must be a good offer."
The 26-year-old moved to St James' Park from Real Mallorca in July 2008 and is still to find the net in 43 games on Tyneside.
Italian giants Roma are reported to be leading the race for his services.