That fee eclipsed the £85.3million Real Madrid paid Tottenham to sign Wales forward Bale in the summer of 2013.
But Bale said: "I'm not fussed and I couldn't care less. None of the players have pulled my leg on it."
Bale has won the Champions League twice in his three seasons at the Bernabeu.
Asked about claiming the record outright, Bale said: "That would be nice. I obviously have a better chance than them as I'm still playing.
"My aim is to win as many trophies as I can and as many Champions Leagues as I can. That will be the aim again this year.
"Everybody wants to beat Real Madrid, but we know we have a chance to make history again and we will be trying our best to do that.
"It is difficult winning the Champions League and not many people get to say they've won it. No matter what goes on in the transfer market you have to have a great season to win the Champions League.
"How much you spend doesn't make a difference, you have to perform on those nights."