Kane has been in scintillating form in 2014-15, with Saturday's brace at QPR taking his tally to 26 across all competitions.
Former England Under-21 boss Stuart Pearce believes the striker should play in the tournament in Czech Republic in June, but Vertonghen has warned Kane against burnout.
"It's difficult for me to judge," said Vertonghen. "Of course England want him. He is a brilliant striker and he can be the main man, but I think he needs his rest for next season.
"It's his call and I know a player always wants to play but sometimes you have to be careful.
"It's a difficult one because last season I played with injuries, but sometimes you just can't. You have to think about what's going to come.
"It's his decision and it's a totally different situation from when I played in 2007. Did that benefit my development as a player? It's hard to tell. I enjoyed playing for my country because I never played international football at youth level.
"So that was my first tournament as a Belgium player and I enjoyed it. It was in Holland and I played in Holland for Ajax at the time, so for me it was brilliant."
