The 32-year-old has been told he can leave the Bernabeu when his contract runs out at the end of the current season.
The Welshman spent last season on loan with Tottenham Hotspur, scoring 10 goals in 20 appearances, but struggled to recapture the form that warranted a move to the Spanish giants back in 2013.
"It is now public knowledge that Gareth Bale will leave Real Madrid at the end of season when his contract finishes, after losing his place in the team during the last two seasons," Rivaldo told Betfair.
“Despite not being as regular as many would expect he leaves the club with a bunch of titles after actively contributing for many of them and I remember well his bicycle goal in the Champions League Final against Liverpool.
“Now, it's time to embrace a new challenge and there are plenty of rumours.
“I think he could even stay in Spain if a good offer arrives from a club with European ambitions, but the most likely scenario should be a return to England to a league he knows well, but that is also more demanding than any other.
“I definitely wouldn't rule out a move to Newcastle as I think there is a chance they might convince him to return to the highest level as one of the stars of the team next season, in what will presumably become a very interesting squad.