The Mirror says 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."