The 28-year-old, who joined the Magpies from Arsenal in 2016, has not played a competitive game for Newcastle since December 2021.
Hayden spent last season on loan at Championship club Norwich City, where he made 14 Championship appearances in a season disrupted by injury.
Since returning to his parent club, the Arsenal academy product has been training with Newcastle's Under-21 side.
With Hayden deemed surplus to requirements at St James Park, he looked set to complete a move to newly-promoted Luton Town earlier this week.
Despite travelling down to Luton to undergo a medical on Monday, the proposed move fell through after the two clubs failed to reach an agreement.
Speaking to reporters on Tuesday, Luton boss said: "We couldn't quite agree a deal, unfortunately. He's someone we had a look at, clearly, there was interest.
"He's a good player but unfortunately we couldn't quite agree a deal. We can have a look and see what else we can do in the next couple of days."
According to the Daily Mail, Standard Liege are now in discussions with Newcastle over a potential deal for Hayden.
The Belgian side have experienced a difficult start to the season after picking up just two points from their opening three league games.
Hayden has also held talks with Championship side Sheffield Wednesday, but a move to Belgium appears the most likely option at this stage.
During his time with Newcastle, the midfielder has featured in 171 matches, contributing seven goals and 10 assists.