Ferguson has confirmed he will end his illustrious managerial career at the end of the season after enjoying an unrivalled 26-year tenure at Old Trafford.
The Scot is unlikely to have many regrets from his time at the helm, but he has regularly acknowledged his failure to sign Gascoigne is among his biggest.
Gascoigne was wanted by United in 1988, but the former England midfielder opted to join Tottenham Hotspur instead from Newcastle United.
"He always says one of his greatest regrets was not signing me, but I think it was the other way round, me not signing for the guy," Gascoigne told Sky Sports News.
"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 the support that Ferguson had shown him during his own foray into management with Kettering Town, and also while he was in rehab in America earlier this year.
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."