Actor and Rangers fan Connery, who was most famous for his role as James Bond in the 1960s and 70s, died last week at the age of 90.
Recalling an interaction with the Scot in the late 1990s, current Napoli manager Gattuso said: “I met him once, at the time the president was David Murray.
“He was a member of the board. It is true, we talked one evening and he absolutely didn’t want me to leave.”
Connery’s son Jason announced on 31 October that his father had passed away peacefully after being “unwell for some time”.
"What can I say? A big hug to all his family and the people who were around him,” Gattuso continued. “I have fantastic memories of him.
“He had a lot of appeal, he was a great character. He made the history of cinema. Always had fond memories of Sean.”
Gattuso, a former Italy international whose playing days are best remembered for his time at Milan, made 34 appearances for Rangers in 1997/98.
The former midfielder returned to Italy after just one season at Ibrox, however.