The Belgian defender praised Eriksen, who he has played with since their time at Ajax, with his form enough to make him a priority for Madrid as they bid to rebuild under Zinedine Zidane.
But despite just a year remaining on his contract, Vertonghen remains hopeful the 27-year-old will remain at Spurs.
"Obviously when the transfer window starts there are a lot of rumours, but there were rumours last year and everyone stayed together, so I'm hopeful," he told Sky Sports.
"Christian is a great player. I have known him since he was 16, played with him since he was 16 or 17 [at Ajax] and I hope he's with Tottenham next season.
"He's an exceptional player."
Eriksen meanwhile recently conceded he would be open to a new challenge.
"I have the wildest and deepest respect for everything that has happened in Tottenham, nor will it be negative," the Dane said.
"But I have also said that I would like to try something new."
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