The 33-year-old has not played a competitive game of football for 18 months, having been released by then-Championship outfit Cardiff City in January 2017.
It's been even longer since he played a run of games, featuring 11 times for Aston Villa as they were relegated from the Premier League at the end of the 2015/16 season, following a terrible season.
Richardson played 45 minutes for West Brom in their pre-season friendly against Barnet last week, and the Birmingham Mail report that he looked to be in 'decent condition' during the game.
The former Manchester United youngster made 12 appearances for West Brom during a loan spell in 2005, scoring three goals before returning to Old Trafford and making a further 60 appearances for his parent club.
He was joined by former Coventry, Barnsley and Huddersfield defender Martin Cranie. Both are said to be training with the club to maintain their fitness, and there is no view to signing a contract at the Hawthorns.
Meanwhile, battering ram striker Salomon Rondon is set to leave the Baggies, with Newcastle United 'closing in' on a deal to sign the 28-year-old. They have already lost highly-rated goalkeeper Ben Foster, who has joined his former club Watford for a fee in the region of £1m.