Kane took his international tally to 10 goals since debuting in 2015 after scoring twice as England eventually eased past Malta 4-0 in World Cup qualifying on Friday.
The 24-year-old striker – on the cusp of a century of Premier League strikes – has scored 125 career goals for club and country, having won consecutive Golden Boot honours in England's top flight.
"I was having some interaction with [Spain head coach] Julen Lopetegui at a game where he was commenting on how lucky I was to have Harry playing," Southgate said. "He's in top form, but he's also got the mentality to want to be the best.
"He knew this morning how many goals in games he had, and also how many Ronaldo and Messi had at this point. He's driven to be one of the world's best. Why can't that happen moving forward?
"I have every trust in Harry. I've worked with him long enough, from the under-21s through, and he'll deliver whatever the occasion. He relishes the occasions. We're still talking about a 24-year-old, so there's still much more to come from him.
"Alan Shearer was 25 [or] 26 when he was top scorer in '96 [at the European Championship]. Harry is still in the early stages of his career, but top scorer in the league two years running and in a really good place."