He is keen to move on in search of regular first-team football having found himself behind Kyle Naughton and Angel Rangel in the pecking order at the Liberty Stadium.
The full-back stood out in Wales’ recent win over Belgium in Cardiff and has attracted interest from a number of Premier League clubs.
Richards, who joined Swansea in 2008, was sent out on loan to Fulham in January before he was forced to return at the end of the campaign as injury cover.
The Wales international had also previously Crystal Palace and Huddersfield.
It is increasingly likely that his appearance for the Swans was his display against Crystal Palace in May, the last of 51 for his local team with the player now in the final year of his contract at the club.
Kit Symons has worked with the 24-year-old at Fulham last term and during his time as assistant boss of Wales.
He made 14 appearances for the Cottagers during his spell in West London.