The Tottenham Hotspur striker came on as a second-half substitute in Kaunas to head home a late winner for the Three Lions in their penultimate Euro qualifier.
And boss Southgate believes the 21-year-old provides a real menace for opponents in the final third, as his squad prepare for Tuesday’s group closer against Moldova.
Watch video highlights of Friday's win over Lithuania
"He’s a goalscorer and is a real goal threat, so he’s someone who is really knocking on the door for us," admitted Southgate, who also has Saido Berahino, Danny Ings, and Cauley Woodrow competing for places up front in his team.
"He’s certainly very much in our thoughts and we knew putting him on at that stage of the game on Friday gave us the option to accelerate.
"If you get the ball into the box, he’s a real danger and he’s a very, very good finisher, which we see all the time in training.
"He works at it and, over the last six months with Spurs, he’s started to transfer that onto the pitch as well which has done his confidence the world of good."
Throughout the campaign so far, England have often played with one central striker as a focal point of the attack and flanked by two forwards who have included the likes of Tom Ince, Nathan Redmond, Wilf Zaha and Friday’s debutant Alex Pritchard.
But when Kane replaced defender Ben Gibson against Lithuania, that provided a different outlook to the team and it was no surprise when the deadlock was broken in the 81st minute by Kane’s bullet header.
Kane headed home England's winner in Lithuania on Friday
"We started with three midfield players [on Friday] which was something we wanted to look at and I think against different sorts of opposition, their movement and combinations were really important to control the game," explained Southgate.
"But when a team sit as deep as they [Lithuania] did, sometimes it’s worth a gamble to put another forward player on and someone like Harry is a penalty box player."
The full England squad trained at the Dariaus ir Gireno Stadium in Kaunas on Sunday morning and they will train there again on Monday before flying on to Moldova in the afternoon.
