Kane has forced his way into the first team at White Hart Lane this term, scoring 14 goals in 22 Premier League appearances.
That form has seen Kane tipped for a place in the England senior team, but he could miss the youth tournament in June as Tottenham look to open talks with the Football Association (FA).
"Maybe I would prefer that Harry has a month's holiday after the season to rest and recover his body and mind," Pochettino is quoted as saying by BBC Sport.
"We need to arrive at a deal with the player and the FA.
"This is my opinion but I realise we need to support the national team and to take the best decision for us all. This is our concern - he is our player.
"The FA need the player to play but at the same time they are concerned about the development of their own young talent."
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