The Times says the referees' union will press Wiley to take legal action against Ferguson after signalling that the Manchester United manager's touchline ban for his outspoken criticism of the official was not the end of the matter.
But Ferguson has sent a written apology to Wiley to reiterate his regret over the personal nature of the attack and hopes that it will be enough to persuade the referee not to sue.
Ferguson wrote to Wiley before his personal hearing in London on Thursday, when he was fined £20,000 and given a four-match touchline ban, of which two matches were suspended, by an FA regulatory commission for claiming the referee "just wasn't fit enough" to officiate in United's 2-2 draw at home to Sunderland last month.
Alan Leighton, the national secretary of Prospect, the referees' union, has claimed repeatedly that Ferguson's remarks were particularly grave because they questioned Wiley's integrity and said that he would sit down with the referee to discuss the matter.
"One of the things we are saying is, is there a case these comments are defamatory?" Leighton said. "I intend to talk to Alan Wiley to see if he wants to sue on the issue."