Taylor's future at Newcastle has been the subject of conjecture this season after finding himself down the pecking order in Alan Pardew's plans.
The 28-year-old, who came through the ranks at Newcastle, has made only 10 appearances this season and clubs are keeping tabs on his situation at St James' Park.
The likes of Valencia and Fenerbahce are thought to be two teams who are weighing up a move for the former England Under-21 international.
Taylor, who has two years left on his current deal at Newcastle, would be loathe to leave his boyhood club, but he could tempted away for a new challenge if he continues to find first-team chances limited.
Agent Jonathan Hope, who is working on behalf of Taylor, told Sky Sports: "There are several clubs who are interested in Steven.
"He has been at Newcastle for 10 years and he loves the club and the fans.
"I think that was obvious from his celebration after scoring last week against Cardiff.
"His focus is on Sunday's game with Liverpool, but interest to secure his services should he leave Newcastle is high."