The 21-year-old opened the scoring during Spurs' 2-1 Premier League win over Burnley at White Hart Lane on Saturday, heading in Nacer Chadli's cross for his 14th goal of the season in all competitions.
It was the striker's third goal in as many games, following strikes against Swansea City last weekend and in the League Cup quarter-final win over Newcastle United in midweek.
And Pochettino believes Under-21 international Kane could be promoted to Roy Hodgson's squad before long.
"I wish for my player the best but Harry has big potential and he's a big talent, why not?" he told BBC Sport.
"If he continues to play in the same way, maybe the opportunity will come for him to play for the national team.
"It's becoming normal now that Harry Kane has scored. We are very happy with him.
"He worked very hard and scored a goal, which is very important for the striker."
Burnley equalised Kane's header with a fine goal from Ashley Barnes, but the hosts were soon ahead again when Erik Lamela produced a sublime strike for his first Premier League goal.
"It was a hard win but after six days it was our third game," Pochettino said.
"It was difficult but we are very pleased with our players. It was a big effort from them.
"Burnley are a physical team with lots of long balls and Federico Fazio performed very well.
"Erik Lamela's strike was special. He is still young and he needs to keep fighting to show his quality."
