The Tottenham forward has been the find of the 2014-15 Premier League season and is currently tied with Diego Costa as the division's top scorer with 19 goals.
At 21 years old, Kane remains eligible to play in England's youth ranks and, with the European Under-21 Championship to take place in June, goalkeeper Hart has urged his new team-mate not to rule out a return.
"I loved my time with the under-21s," said Hart. "We had a great thing going and, from what I understand speaking to Jack [Butland, the England under-21 captain], it is the same thing going on right now with the under-21s.
"It is the place where they want to be and they want to win the tournament. I can only speak from my personal experiences and I really enjoyed the two tournaments that I went to.
"It was a little bit different for me - I wasn't really knocking on the door for a starting place in the first-team. I had little bits of experiences with the first team but it never crossed my mind that I wouldn't be involved in the summer.
"I can't speak for Harry [Kane] but I'd imagine he would be very excited to represent his country in the summer.
"There is so much to gain from playing in the tournaments, apart from the sheer enjoyment of playing tournament football for your country at a very high level against high-quality players.
"I think we have all seen the blueprint of Germany. That is quite inspirational and I am sure [England under-21 manager] Gareth Southgate will be alluding to that when he talks about drawing people to play for his U21 side."
England have won all four of their Group E fixtures so far and sit six points clear of second-placed Slovenia.
Lithuania are tied on six points with Slovenia and Switzerland but, after opening their campaign with back-to-back victories, have lost their last two matches without scoring.
England will be without Daniel Sturridge (hip) and Adam Lallana (groin) after the pair withdrew from the squad earlier this week, but Ryan Mason could join Tottenham colleague Kane in making his full international debut.
Aston Villa's Fabian Delph is battling to overcome illness ahead of Friday's fixture.
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