Giggs, who will work as Louis van Gaal's assistant manager at Old Trafford next season, was reported to have had a secret affair with Natasha Lever, who is the ex-wife of the sportsman's younger brother Rhodri.
Giggs's father Danny Wilson, who is planning to marry long-term girlfriend Dawn Pritchard, will have Rhodri as his best man, but Giggs is not allowed to attend unless he apologises for the affair.
"I'm going to get married in a small ceremony," the Daily Star quotes Wilson as saying. "Rhodri will be my best man but Ryan won't be invited.
"He's not welcome unless he shows some remorse. Sorry goes a long way."
Giggs announced his decision to retire from playing professionally shortly after being handed the assistant manager's role at Old Trafford last week.