The Dragons are currently top of Group B having collected seven points from a possible nine so far, putting them on course to end a run of 56 years without qualifying for a major tournament.
Real Madrid star Bale has played a key role for Wales in the early stages of the campaign, and Giggs is confident that his compatriot can continue to deliver on the world stage.
"He's stepping up – he has to deliver at Real Madrid where the expectation is huge and the pressure is on and it's showing in his performances for Wales that he can still deliver," the former Manchester United winger is quoted as saying by Wales Online.
"It's been a massive learning curve for him over the last season but he's lived up to every expectation and more. Not only that he's a great lad who wants to get better and wants to be the best.
"And I think he could be the best we've had. He can be as good as he wants to be because he's such an amazing talent. He can go all the way."
Wales continue their Euro 2016 qualification campaign with a trip to face group favourites Belgium next month.