The 27-year-old brought up his double century — in his 300th appearance for Spurs — with his 12th goal of the season in Thursday’s 3-1 away win over Bulgarian side Ludogorets in the Europa League.
Greaves and Bobby Smith are the only other two players to have scored more for Spurs.
“The numbers make him a club legend, with what he is achieving in the Premier League and all competitions is great for such a young guy,” Mourinho told BT Sport.
“Tonight, 45 minutes one goal and one assist (for Lucas Moura’s goal, taking Kane to double figures for assists this season). I believe he can. It’s just a matter of time.”
Kane’s first goal for Spurs came in the same competition in 2011 against Ireland’s Shamrock Rovers.
But it took him another three years to establish himself as a regular starter and he spent time on loan at a number of clubs, including Leicester.
Kane said records were not on his mind but promised to keep the goals coming.
“(Beating records) is not on my mind. You guys will let me know when I get the next one, but it is hard to take in when you are playing, I think once you finish you take it all in.”
Kane’s achievement was hailed by former Spurs greats Gary Lineker and Glenn Hoddle.
“What an achievement for @HKane scoring his 200th goal for @SpursOfficial in his 300th game. Well played,” tweeted Lineker.
Hoddle said Kane should pass Greaves’ record provided he stays at the club.
“I’m delighted for him,” said Hoddle on BT Sport. “Look at those players there, (Bobby) Smith and Jimmy Greaves are only ahead of him.
“I think if he stays at the club I think he could actually catch Jimmy.”