Amid the cheating scandal, lower than expected performance and the fight to retain Jenson Button, the Prodrive boss is speculated to be in the frame for Nick Fry's job.
UK publication People said the Englishman is "deep in negotiations" and could - although the team is banned from racing there - be confirmed at Monaco on Friday.
"With Richards' wealth of experience," a team 'insider' claimed, "we can look forward to a calming influence."
In another tabloid newspaper, meanwhile, it is reported that 25-year-old Button got over the break-up with his fiancée by going out with British 800m runner Emma Davies.