Britton found playing time hard to come by last season after injury and the arrival of Jack Cork.
Leon has made a career total of 415 appearances for Swansea but started only 6 league games during season 2014/2015.
Should Britton be lured by the American dollar the club would be unlikely to stand in his way for a nominal fee after 12 years of service interrupted by a brief spell at Sheffield United.
The 32-year-old has two years left on his contract but it seems he won’t be happy on the sidelines next season and is currently looking at all options home and abroad.