The new Tottenham boss has already been linked with a potential swoop to sign the Real Madrid forward in the January transfer window following Mourinho’s appointment on Wednesday morning.
Mourinho has been tasked with reviving Tottenham’s fortunes, with the north London side in 14th place in the Premier League table after 12 games this term.
Bale was regularly linked with a move to Manchester United during Mourinho’s two-and-a-half year stint at the 20-time English champions but a deal failed to materialise.
The Welsh winger is out of favour at Real Madrid under their current manager Zinedine Zidane despite contributing to their success under the Frenchman since his arrival in 2013.
Bale upset Real Madrid supporters by holding a controversial banner after Wales qualified for Euro 2020.
Former Spurs boss Redknapp believes the signing of Bale would be a great way for Mourinho to secure the support of Tottenham fans.
“What a signing he’d be for the club. What a signing,” Redknapp told talkSPORT. “That would get him on side straight away, the fans would love that.
“That would be an amazing move for him.”
Bale moved to Real Madrid from Tottenham in a £85.7m deal in the 2013 summer transfer window.
The Wales international scored 55 times in 203 games in all competitions for Spurs.
Bale has won the La Liga crown as well as three Champions League titles at Real Madrid.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news