The Real Madrid star hinted after his heroics in the Champions League final last month that he will discuss his future this summer.
United have regularly been linked with the Wales attacker, and now his national team manager has backed the former Tottenham Hotspur star to thrive at Old Trafford.
"I'd be a happy United fan, that's for sure," Giggs told the South China Morning Post. "I think he's a Man United player. I think the fans would love him. The fans would adore him but again, like I say, he's at a club where he's won three Champions Leagues so why would you leave?"
Bale was the most expensive footballer in history when he signed for Los Blancos from Spurs for £85m in 2013.