This is according to The Metro who cite reports from The Guardian that suggest the defender has decided to reject an offer of a new contract and a pay increase at Manchester City and further claim that the Reds are expected to go back in for his signature at the end of the season.
25-year-old Richards made his debut for Manchester City in 2005, forging a promising reputation as one of the Premier League's top and most versatile young performers and going on to win 13 senior international caps for England.
However, his career appears to have stalled somewhat in recent years, chiefly due to a combination of persistent injury woes and also being stuck behind the likes of Pablo Zabaleta in the pecking order at the Etihad Stadium
Indeed, Richards has made just two appearances in the Premier League this season, with the last coming in the win over Sunderland in November.
Liverpool - who currently sit top of the Premier League table with just five games of the 2013/14 campaign remaining - have been mightily impressive in an attacking sense under Brendan Rodgers this year, yet obvious questions remain over the quality of the defensive unit at Anfield.
Liverpool could well face competition for his signature with Arsenal - as well as the likes of West Ham and Newcastle - viewing the player a contender to replace Bacary Sagna.
Arsenal could well have the need to invest in a new long-term right-back option this summer, with the future of Gunners stalwart Sagna still evidently undetermined.
With the Frenchman out of contract in just a few month's time, it is as of yet unclear whether he intends to remain at the Emirates Stadium any longer and, despite a chronic lack of first-team football in recent months, Richards could prove a sufficient replacement for Arsenal and Arsene Wenger.