Madrid have emerged as a possible destination for Eriksen after the Tottenham star revealed he wants to "try something new" .
That statement rapidly led to links to Real Madrid, who have already spent big this summer to sign Luka Jovic and Eden Hazard in attack.
"Obviously when the transfer window starts there are a lot rumours, but there were rumours last year and everyone stayed together, so I'm hopeful," Vertonghen told Sky Sports News.
"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 arrived from Eredivisie giants Ajax in 2013 and the 27-year-old has established himself as one of the Premier League and Europe's best midfielders.
The Danish midfielder, who has earned 89 caps for his country, has made 276 career appearances during his time with Spurs, scoring 66 goals during his six-year stay with the London club.
Eriksen fired 10 goals in 50 appearances for Spurs this campaign, including two in Champions League play.
However, Eriksen has not won silverware with Tottenham after reaching the 2015 EFL Cup final and this year's Champions League decider.
Prior to joining Spurs, Eriksen played at Ajax, winning three Eredivisie titles as part of a five-trophy haul with the Dutch club.
The midfielder was on the mark on Monday, scoring from the penalty spot as Denmark topped Georgia 5-1 in a Euro 2020 qualifier.
Eriksen was joined on the scoresheet by Martin Braithwaite, Yussuf Poulsen and Kasper Dolberg, with the latter firing a brace.