The former Manchester United winger, currently preparing for a Euro 2016 semi-final against Wales, left Old Trafford for Fenerbahce last summer after a season on loan at Sporting Lisbon.
However, Potters boss Mark Hughes is keen to bring the 29-year-old back to England, although he faces competition from Valencia.
“I know there is an interest there. Valencia are a big club but it is the draw of the Premier League,” assistant manager Mark Bowen told talkSPORT.
“He is player that Mark admires a lot and he has had a very good tournament.