Edwards has been at Molineux since January 2008, since when the 31-year-old has made 307 appearances in all competitions.
However, the Welsh international is not regarded as first choice in the Wolves midfield by head coach Nuno Espirito Santo, and it appears that a Championship rival is trying to take advantage of his situation.
According to the Reading Chronicle, the Royals have made an approach for the long-serving player in a bid to improve their squad before the end of the transfer window.
Last season, Reading only missed out on promotion to the Premier League in the playoff final, but the Berkshire-based club have only registered four points from their first four fixtures this season.
Edwards will be reunited with former Wolves teammate Jon Dadi Bodvarsson should he make the switch to the Madejski Stadium.