Gutierrez, who has struggled with injuries for much of the season, has made only two appearances for Alan Pardew's side this campaign.
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"There is an interest in Jonas Gutierrez but there's nothing to confirm at this moment," Hughton said on Monday.
"If that changes, we will let you know."
Posts from a Twitter account in the name of Gutierrez at the weekend appeared to suggest his time at St James' may soon be at an end.
"It was an honour and a pleasure to play with the newcastle shirt," read one post, while he also stated: "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 moved to Newcastle from Mallorca in 2008 and suffered relegation from the Premier League in his first season at the club.
However, he was a regular starter under Hughton as Newcastle returned to the top flight a year later, and has made 140 appearances in total for the club, scoring six times.