Joe Ledley has turned down offers from two unnamed clubs in the Championship.
The Wales midfielder, who has 73 caps, has also had offers from Spain, Israel, China and Turkey.
Ledley left Crystal Palace at the end of last season after he rejected their offer of a new one-year deal.
The 30-year-old is expected to be named in manager Chris Coleman's squad for the World Cup qualifiers against Austria and Moldova next month, whether he has a new club by then or not.
He has been linked with a return to two former clubs, Championship Cardiff City and Scottish champions Celtic, though Bluebirds boss Neil Warnock has played down the link.
Ledley, who joined Palace in 2014, said early in the summer that he would consider a switch to another country or division.
"It doesn't bother me (playing in the Premier League) I have been there three-and-a-half-years so maybe a new challenge would be good," he said. "I have only just turned 30."