Fulham looked like signing the defender, after the Swans accepted a £500,000 bid from the Cottagers according to BBC Sport, but his recent international performance against Belgium has put him on the radar of Premier League clubs.
Richards made just his fourth Wales appearance during the country's superb 1-0 win over Belgium last weekend.
Playing on the right side of midfield, he helped nullify the Belgian's superb attacking threats, with Premier League Player of the Year Eden Hazard unable to influence the game to the degree he'd have liked.
Richards' contract expires next summer, and both West Brom and former loan club Palace are the top flight sides interested in securing him according to the Mail.
The 24-year-old has struggled to establish himself in the Swansea side since they were promoted, despite having long been on the periphery of the squad.
He started the last two games of the season, but only seven throughout the entire league campaign, instead spending much of his time on loan, much like he has done since getting to an age when he would be expected to be playing.
Richards was at Fulham last season, after spells at the Eagles and Huddersfield the seasons before, and he has just 51 appearances for the Swans in total since making his debut six years ago.
But the high profile performance against a side ranked number two in the world has reminded suitors of his quality, and Swansea are listening to offers for the Wales international.