Ferguson believed that he had captured Gascoigne's services when he was due to leave Newcastle United in 1988.
However, the former England international opted to join Tottenham Hotspur at the last moment.
"I would love to have signed Paul Gascoigne," Ferguson told BBC Radio Five Live. "I think I could have done something with him, he's the one real world star England have produced.
"Gascoigne was the one that got away."
Gascoigne went on to represent a number of clubs, including Lazio, Rangers and Middlesbrough.