Gascoigne looked set to move to Old Trafford in the summer of 1988 after he became frustrated with the lack of ambition being shown by then club Newcastle, but ultimately joined Spurs and remained there for four years before moving to Lazio.
Sir Alex, who announced his retirement on Wednesday, said on numerous occasions in the past that not signing Gascoigne is one of his biggest regrets, and the 45-year-old Geordie says the feeling is mutual.
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"I've been watching some of his documentaries of what he's won and what he's achieved. There are only a couple of managers when I played who I would love to have been in the dressing room with and he's certainly one of them, to have seen what he would have been like.
"I know I would have had a lot more trophies in my cabinet if I went with him. It was a massive missed opportunity.
"Obviously I worked with a great manager in Terry Venables, don't get me wrong, but I just think the players around about my age when I had the chance to sign for them and what they've achieved.
"It's not just on the field, but off the field as well. He doesn't just work with them at the club, he works with them when they're not at the club.
"The guy is just unbelievable really. It's really sad and I had a tear in my eye when I heard. He is just one of those guys who you wanted to win everything and he has done.
"It's so sad that we're not going to see him on the touchline or on the bench."
Gascoigne also revealed that during his brief stint as Kettering manager, Ferguson was among the few people willing to give him advice when the going got tough.
He added: "He was one guy that, when I was a manager at Kettering, even though I didn't last very long, whenever I was struggling I'd call him up and he'd spend time on the phone and tell us what to do. He was fantastic.
"The last memories I had of him were not long ago. When I was in treatment five months ago, he sent over a DVD message saying to 'come on, pull through, you can do this'.
"This is when Manchester United are through the season and wanting to win the league, and that he took time to come on a DVD and say words of encouragement shows how special the man is."