Redknapp, who helped develop Bale at Tottenham, thinks luring him back would be one of the best first moves the new Spurs manager could make.
"It could be couldn't it, yeah," Redknapp said on talkSPORT Wednesday morning.
"What a signing he'd be for the club. What a signing. That would get him on side straight away, the fans would love that. That would be an amazing move for him."
Bale was linked countless times with a move to Manchester United when Mourinho was in charge at Old Trafford.
In the summer of 2017, he said he would "fight" to sign Bale before eventually conceding defeat in the August of that year when he said: "I think now everybody knows he is going to stay."