Ferguson met actor Craig's mother on an aeroplane flight to the United States and said he is welcome to visit Old Trafford.
But his mother responded by telling Sir Alex that Craig would do no such thing as he supports the club's fierce rivals.
"I know Daniel Craig. The only thing about Daniel Craig is he's a Liverpool fan," report The Sun.
He continued: "His mother was on the same plane as me when I went to New York in September.
"I said to her, 'There's a ticket for Daniel at Old Trafford any time.' She looked at me as if I had horns on my head! She replied, 'I don't think Daniel will want to go and see United.'"