Kane was on target twice for Tottenham in their 2-1 Premier League win at QPR on Saturday, taking his tally to 26 for the season with Hodgson in attendance at Loftus Road.
England resume their Euro 2016 qualifying campaign against Lithuania in under three weeks' time before facing Italy in a friendly.
"I've just got to keep doing what I'm doing," Kane said.
"There are still a few games before the international break and I want to do the best I can for Tottenham.
"That's what I'm looking to do. Get some more wins between now and then and we'll see what happens.
"Any English player would love to play for England – it would be a dream – but there are a lot of great players in England.
"I just have to keep concentrating and do the best I can for Spurs."
