The Chelsea manager believes the Spanish giants will be getting themselves a "fantastic player" if the Tottenham star's proposed move to the Bernabeu goes ahead.
However, Mourinho also warned Bale of the pressure that will be on him to justify his transfer tag, with Real reportedly set to pay a world-record fee for the 24-year-old.
"I asked the club to buy him last season but it was not possible," said Mourinho.
"It looks like it is happening this season so I am happy for them because they get a fantastic player but, of course, the numbers are huge numbers and the kid has to go now and there's pressure to prove that he's worth that investment."
Mourinho believes Bale would have flourished in his Real side and expects his successor Carlo Ancelotti to make the most of the Welshman's talents if he moves to Spain.
"I think he's a fantastic player and the way my Real Madrid was playing, I think it was an easy player to fill a space and to get into that tactical dynamic," said Mourinho.
"I don't know what Carlo is thinking now but Carlo is an experienced coach and for sure will get the best out of him."