The Tottenham Hotspur striker has been one of the top performers in the Premier League this season, as well as for Southgate’s Under-21s.
And having worked with the 21-year-old so closely over the last 16 months, Southgate is not surprised to see Kane leading the top English goalscorer charts.
Kane has been in good form with club and country this season
"I am never surprised, because I have seen the way that lads can make rapid progress in such a short space of time and it can happen at any period," said Southgate, who takes the Under-21s to his former club Middlesbrough for a game with Germany in March.
"With Harry, he is a really good trainer so you know that he’s got a chance because he will always want to work at his game.
"He has always been a really outstanding finisher and I think he is now transferring that into matches and part of that is confidence.
"I also think that this year he looks really good physically and I know the way that Mauricio [Spurs boss Pochettino] works and I am sure the sessions they are doing on and off the training ground will have helped that.
"We saw with Southampton last year that Mauricio is not afraid to give people a chance if they are doing well – with Harry and Ryan Mason, who is too old for us now, he is giving them their opportunity and Harry is keeping some outstanding players out of the team.
"I have told him to save a few [goals] for us, but it’s brilliant experience for him."
Kane’s progress has already seen him rewarded with two new contracts at White Hart Lane so far this season and he’s rapidly become one of the key players in Pochettino’s squad.
And it is the versatility which the Walthamstow-born ace has illustrated that has caught the eye for Southgate, as well as the strong character and mental strength required at the top level.
See the striker's goal for the Under-21s in Kaunas
"I never like to say ‘he’s the next whoever’ because they are individuals really," revealed Southgate.
"His link play is very good, he’ll create goals for people, he can play No9 or No10, find space, drop into space and his hold-up play is good.
"He was a bit unlucky in the summer, he had a run in the team and got injured playing for us at Swansea, so he missed Toulon.
"But straight away in September he scored for us [in Lithuania] and scored in the next one [in Moldova] and really played well in the play-offs against Croatia.
"So he’s in a great place at the moment, as is Danny [Ings] who is going to improve and improve because again he has the right mentality and the right mind-set at a club where again the ethic is good, to work and learn.
"But you’ve seen the group and you could pick out any number that have got that mentality really."
As well as the game with Germany next month, Southgate’s side will also make an early trip to Czech Republic to face the nation who will host this summer’s Euro Finals for which England will compete.
Kane's goals have made him an integral part of Spurs' team this season
But with Roy Hodgson’s squad also in action with their own Euro Qualifier against Lithuania at Wembley and a trip to face Italy in Turin, Kane can’t have failed to catch the senior manager’s eye.
"That is Roy’s call," admitted Southgate, who has also seen the likes of Luke Shaw, Raheem Sterling and Saido Berahino graduate from his group into the senior squad.
"That will depend on how others are doing and if he is still delivering when we get nearer that time.
"It’s been brilliant how he has kept his form for quite a sustained period, so let’s hope he can continue that.
"There is no reason why he wouldn’t come with us in the summer.
"It’s easy for him to do both. I think he falls in that category where he’s been with us right the way through and I think he would want to come and be on that stage really.
"That’s still a terrific stage when you look at some of the players in the last couple of tournaments that have come through the latter stages, of all the Spanish group, Thiago and Isco and Verratti with Italy, some of the French boys that won the U20s, like Pogba, so it’s a great stage for young players to test themselves."
