The 29-year-old has been a free agent since leaving Burnley in the summer, after five years at the Lancashire club, where he was named club captain in 2024.
He scored 18 goals and got six assists from midfield in 42 Championship appearances for Burnley last season as they earned automatic promotion back to the Premier League.
Wolves are keen on adding another midfielder before the transfer window closes at 7pm on Monday and due to the space in their registered Premier League squad, the club are likely to target a homegrown player for that position.
Fellow Englishman Hayden Hackney, who is currently top of tier two with Middlesbrough, is another midfielder of interest to Wolves as they aim to improve the options available to Vitor Pereira.