After Bale helped Madrid to beat United 2-1 in Tuesday's UEFA Super Cup, Mourinho claimed it was "game over" for his hopes of signing the forward, who has been linked with a move to Old Trafford amid talk of Monaco's Kylian Mbappe joining the European champions.
The United manager had said ahead of the match in Skopje he would consider the Wales international to be available if he were left on the bench, only to see him start.
Bale wants to stay at Madrid, but was full of praise for Mourinho after the match, tipping the Premier League side for a "fantastic" campaign due to the presence of the former Chelsea boss.
The 28-year-old feels Mourinho, who is starting his second season, is bringing United back to the level at which they belong.
"I think it [the fear factor] is getting there," Bale told reporters when asked about United.
"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.
"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.
"United did very well. They gave us a difficult game and I'm sure they'll do fantastic this season. I see no reason why they can't [be a force in the Champions League]."
Super Cup x 3 pic.twitter.com/hbasQtMo7r— Gareth Bale (@GarethBale11) August 8, 2017
Despite his positive words about Mourinho, though, Bale continues to insist he is happy at Santiago Bernabeu despite the constant speculation.
"I don't want to move," he said. "The club are happy with everything. Everything has gone as normal like it has every year.
"We enjoy winning games, we enjoy winning trophies and we're hungry to win everything. Like any footballer, you want to win as many trophies as you can, so that’s the main thing."