Souness had an ultimately ill-fated spell in charge at the St. James’ Park club.
The former Liverpool player and manager had been hoping to bring the club back to its glory days.
In an interview with cardplayer.com Gascoigne said: "I remember when Graeme Souness was manager. I’m in my apartment in Jesmond, and I think it was Thursday, or Friday night it was, or something like that.
"My phone rings and it was Graeme Souness. He said, ‘Gazza, where are you?’ I was just up the road from the restaurant he was at with his wife. He wanted me to come and see him as he wanted a word with me.
"I felt sorry for him. I went to the restaurant and I saw him sitting there and I sat next to him. I asked him what he wanted. He asked me how to win the fans over.
"I think it was because he dropped Alan Shearer. You don’t do that. Ruud Gullit did that as well. You can’t do that to a legend. That would have hurt Shearer.
"You don’t do that to players of his status. He’s a guy who’s able to lead well. Absolute legend of the club."