Redknapp was in charge of Spurs when Bale’s career ignited and he became a talismanic presence with the ability to tempt Madrid into a record-breaking move.
Now 29 years of age, the fleet-footed frontman has enjoyed plenty of highs at the Santiago Bernabeu, including four Champions League triumphs, but has also suffered a number of lows.
Bale has fallen out of favour under Zinedine Zidane and is expected to be among those moved on by Real in a summer of much change for the Blancos.
Redknapp is looking for an English top-flight side to do a deal, with there an admission on his part that Old Trafford or north London would be suitable landing spots for a world-class performer.
“Whoever signs him will be signing a fantastic player,” Redknapp told the Daily Mail.
“Any club he can go to he can make a difference - he can turn any club around.
“He would be a great signing for anyone - Man United could do with Gareth Bale.
“There's not a club in the country where he wouldn't make a massive impact. I think he's an incredible talent.
“Anybody who gets Gareth Bale is going to lift them. If it's Spurs, Man United, whoever it is, it would be an amazing signing for them.”
As things stand, Bale is still tied to a contract with Real through to 2022, but it is looking increasingly unlikely that he will see that agreement out.
A move is expected to be made over the coming months, with it even being suggested that Madrid could sanction a loan switch for a player they are now actively seeking to get off their books.
If he is ushered through the exits, then Bale will depart having scored 102 goals in 231 appearances for the Blancos.