Britton made just nine appearances in the 2014/15 Premier League season and is understood to be interested in a move to MLS.
The 32-year-old midfielder has played second fiddle to the likes of Jonjo Shelvey and Jack Cork this season. His knee injury kept him out for a large chunk of the campaign and he has failed to break back into the first team after moving down the pecking order.
Britton would be joining the likes of Steven Gerrard and Frank Lampard who make the switch following the 2014/15 Premier League season. Gerrard and Lampard are set to link-up with LA Galaxy and New York City FC respectively in July.
The Swansea man has been with the club for the best part of 12 years, having left for one season to Sheffield United in 2010/11, only to rejoin The Swans, where he has been since 2002.
It seems that he could be leaving for a new challenge this summer transfer window with MLS the most likely destination.
Will Leon Britton make the switch to Major League Soccer?