Davies has spoken with Cleverley
Cleverley faces around four weeks on the sidelines as a result of the incident in Saturday's Barclays Premier League clash at the Reebok Stadium.
Press Association Sport understands veteran forward Davies, 34, did ring Cleverley on Saturday evening to wish him all the best.
It was initially feared the 22-year-old had broken a bone and could have been out for much longer.
Messages posted on a fake Tom Cleverley Facebook page on Saturday night claimed the United player was angry and that Davies had not apologised.
United made clear this account was not genuine and Davies' wife, Emma, who herself received abusive messages via Twitter, tweeted to say there had been contact.
Her tweet read: "For all the ill-informed haters... Kevin spoke to Tom Cleverly (sic) on the phone earlier. He would never intentionally hurt anyone."
Cleverley underwent a scan on Sunday which confirmed the injury was not as bad as first thought.
The youngster will miss the start of the Champions League group stage and a possible England debut in next month's Euro 2012 qualifier against Montenegro but should be back in action in November.
Related Manchester United News