The former Tottenham goalkeeper believes an agreement could be reached which sees a Danish playmaker replaced by a Welsh forward in north London
The Denmark international playmaker has been heavily linked with the Blancos in the past.
Speculation during the current transfer window suggests that the 27-year-old, who continues to run down his contract in north London, could be heading to Serie A side Inter .
No agreement is in place, though, and the door remains open for others to make a move.
That could see Madrid join the race for a creative midfielder who has thrived in English football since joining Spurs from Ajax in 2013.
If an approach is made from the Spanish capital, then Robinson would like to see Jose Mourinho ask a question of Bale.
The Wales international forward is said to be unsettled at Santiago Bernabeu, with a return to the Premier League having been mooted for some time .
An ideal opportunity to make that happen may have presented itself, with there a chance that Real may be willing to trade Bale for Eriksen.
“I think they should try to get him if they can,” ex-Spurs keeper Robinson told Football Insider of Bale.
“I think if Eriksen is going to go to Real Madrid, I think that would be the perfect deal for Tottenham and Tottenham supporters.
“He’ll be the perfect fit for Mourinho, he’d give the whole place a lift, rather than have Eriksen who clearly doesn’t want to be there.
“He’s sulking and he’s not happy, it looks like he is going to want to leave.
“To get someone of Bale’s quality in, as part of a deal, if that’s possible then it’ll be great.”
Bale was back in Madrid’s starting XI for their 3-0 victory over Getafe on Saturday .
He drew a blank in that contest and has only registered two goals for the Blancos this season.
Eriksen has bettered that return at Tottenham, contributing three goals and as many assists in 2019-20, but has seen the uncertainty surrounding his future limit his game time and a move is expected to be made at some stage.