The former England star departed Newcastle United in 1988 but joined Tottenham instead of United and he admits it is one thing he certainly rues in his football career.
"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."