The 31-year-old is currently without a club after he was released by Aston Villa at the end of last season.
Villa's fierce rivals Birmingham are said to have failed in their bid to land the Premier League veteran earlier in the summer.
And now the Mirror claim Leeds are considering a move for the former England international as manager Garry monk looks to add experience to his squad.
Richardson is said to have been training with Championship rivals Bristol City in a bid to earn a contract, but Leeds have since showed an interest.
GETTY
Garry Monk looking to add experience to Leeds squad
Richardson rose through the ranks at Manchester United and helped Sir Alex Ferguson's side to the 2006/07 Premier League title, the FA Cup and Community Shield.
United offloaded him to Sunderland in 2007 for a reported £5.5million before two disappointing stints at Fulham and Aston Villa - both of which resulted in relegation.
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