The Red Devils boss Mourinho, who is keen to bloster his side, revealed his interest in the Los Blancos star earlier this week. But Bale has repeatedly said he is happy with life at the Bernabeu.
However, the Wales international is convinced United are getting better and will be contenders on all fronts this season.
“United did very well (in the Super Cup). They gave us a difficult game and I'm sure they'll do fantastic this season,” said Bale as the Mirror reported.
“I think it's getting there, obviously I think by bringing Mourinho in, it's kind of boosted the club, by winning a few trophies last year, it did them great, and I think they're getting back to where they belong.
“I see no reason why they can't do well in the Champions League, he's a great manager, he's done everything in football, he knows what he's doing and I'm sure he's building a great team for what he hopes to achieve there.”