Owen was released by United earlier this summer after three seasons at Old Trafford which were plagued by injury woes.
Stoke are understood to be leading the race for the 32-year-old former England international, who managed just four appearances for United last season, with his last on November 2.
Via his Twitter account, Owen said: "Getting closer to finding a new club. Had a good deal of interest but just need to pick right! Can't wait to get going again."
Everton have also been rumoured to be keen on Owen, despite his former allegiance to Liverpool where he spent eight seasons up to 2004 before moving on to Real Madrid, Newcastle and then United.