Shearer twice turned down Alex Ferguson's offer of a move to Old Trafford in the mid-1990s, choosing first Blackburn and then Newcastle.
And Giggs and Neville still cannot believe the former England skipper, who only won one Premiership title with Blackburn in his career, rejected the chance to join United.
"Both Ryan and myself can never understand why any player would ever turn down Manchester United for Blackburn or Newcastle," said Neville.
"Other players we missed out on recently are Ronaldinho and Arjen Robben, but I'd have to say Shearer was the one we wish we'd got.
"I played with him in England games and he definitely had the mentality of a United player. Why he never came to United, I do not know.
"I can't understand that decision and I can't begin to understand what must have been going through someone's mind when they choose Blackburn and Newcastle over United."
Giggs, who has won eight titles, four FA Cups, the European Cup and League Cup during his career at United, would have relished the chance to play with Shearer.
Giggs added: "He was just an unbelievable goal scorer and as a winger, to be supplying the ball to someone like that would have been a dream. He was certainly a world-class player."
--------------------------------------------------------------------------------
I can't believe this is still bothering them.