Kane is wanted by his side, England's Under-21s and the senior national team over a similar time period.
England play the Republic of Ireland in a friendly on June 7, then travel to face Slovenia on June 15 in a Euro 2016 qualifier.
The forward could also be selected in the squad for June 17's European Under-21 Championship.
While Spurs will be playing a friendly in Malaysia on May 27 and again in Australia three days later.
Coach Pochettino confirmed that Kane would be travelling with the team on their Asian Tour.
"Sure, because he deserves to go.
"He will enjoy seeing a different country and it is one week to enjoy with our supporters in Australia and Malaysia, so he deserves to go," he said.