Allen, who scored 60 goals in 105 appearances for Tottenham between 1984-88, was pouring praise on the 21-year-old on Alan Brazil Sports Breakfast.
The retired striker was part of the Spurs coaching staff while Kane was coming through the ranks as a youngster, and says that he would be more than worthy of a chance in the England squad should the call come from Roy Hodgson.
Allen said: "It is great to see a young English striker scoring goals in the Premier League. Harry is single-minded in the right way and I think it is fantastic.
"People are starting to talk about him making the England side. That would be a meteoric rise and it would be nothing more than he deserved because he has worked hard to get to where he is."
Kane netted his 12th goal of the season in all competitions in Tottenham's 4-0 Capital One Cup thumping of Newcastle United last night.
The youngster has been a key figure in many of the England youth squads having represented the Under-17s, Under-19s, Under-20s and Under-21s; for the latter he has scored eight in 10 appearances.
His goalscoring form in the league isn't quite as impressive as his overall tally suggests as he has only hit the back of the net three times in 12 Premier League games this season.
Nonetheless, you would have to think Kane will be in with a real shout, especially considering Liverpool striker Rickie Lambert is consistently selected by Hodgson despite only scoring a paltry two goals in 18 appearances in all competitions this campaign.