The Wales international’s future at los Blancos has been a source of speculation in recent months after falling out of favour at The Bernabeu.
Bale was an unused substitute in Real Madrid’s 2-1 win against Bundesliga giants Bayern Munich in the first leg of their Champions League semi-final on Wednesday night.
Indeed, the 29-year-old appears to have fallen behind Luis Vazquez, Isco and Marco Asensio in the pecking order under manager Zinedine Zidane.
Manchester United have been regularly linked with a move to sign the former PFA player of the year from Real Madrid since Jose Mourinho took over the reins at Old Trafford in May 2016.
Bale completed what was a world record £85m move to Real Madrid from Tottenham in the 2013 summer transfer window.
The Welsh forward has won three Champions League titles, the Copa del Rey and La Liga since his switch to the Spanish top flight.
His former Spurs manager Redknapp is hoping that Bale will consider a return to Tottenham in the summer transfer window if the Real Madrid star does opt to leave the Spanish capital.
Gareth would be a great signing for Tottenham, it would be fantastic,” Redknapp told talkSPORT.
“He’s an amazing player. He can play so many positions and in so many systems, there are so many strings to his bow, he’s such a fantastic talent.
“Going back to Tottenham – if he comes back [to the Premier League] he would only go to a top-six club, but it would be nice to see him go back to Spurs.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news