The Red Devils boss also revealed that the club are yet to have drawn up a shortlist of potential candidates to replace the Scot but had words or praise for David Moyes
Sir Alex told BBC Radio Five Live: "I would have like to have signed Gascoigne, I’d have loved to have got Gascoigne. He played against us up at Newcastle, he’d be out of the team for weeks, and they were down the bottom.
"We went there Easter Monday, and he was starting to get [recognised]. We’d known that because we’d scouted him and thought 'Gascoigne’s the man', and we couldn’t get near him, honestly it was unbelievable.
"I wish I’d have got him, I maybe could have done something with him. If you look at English football since say 1966 when they won the World Cup, you’d have to say Gascoigne’s been the one real world star that England have produced.
"I know Wayne Rooney’s coming hopefully towards that, and once he gets the maturity."
Ferguson also stated that the Red Devils have yet to draw up a shortlist of candidates to replace the Scot and suggests that the situation in terms of how well managers are performing could be different when he retires.
He added: "No, never discussed [a shortlist]. It’s a dangerous game that.
"At this moment in time there are maybe half a dozen managers doing very well in the Premier division. Only half a dozen because all the rest are fighting for their lives.
"Some are doing great jobs with the resources they’ve got. [David Moyes] Unbelievable, unbelievable. What he’s done at Everton is quite miraculous really.
"As we speak today, is that going to be the same in two years’ time when I’m ready to quit? You can bet your life that some of them will have lost their job. So trying to anticipate, that they’re doing well at the moment but will they in two years’ time.
"We need to have someone experience, no doubt."