Kane turns 28 in July and will have two years remaining on his current Spurs contract. The club are adamant he is not for sale but another season without silverware would but heighten talk the England captain may need to leave north London to pursue his dream of winning silverware.
Asked if there was a danger Kane, who has been linked with a move to Manchester United and Real Madrid among a host of other sides, could allow his club future to influence performances this summer, Southgate said: "He's so focused. I had a chat with him, as I do with all of the players when they come into the camp and he's very positive about the club.
"He was talking about only being a couple of points off the Champions League, League Cup Final and you can see his focus in the game the other day. He scored a fantastic goal, an excellent assist as well. I've got no worries about Harry Kane. He's a fantastic professional, his focus is always on the next training session, the next match and he is someone who can absolutely put anything to one side.
"Harry is of course a highly motivated player and all players want to win things. He has got an opportunity with his club in the next few weeks to do that. I've got four players in the other dressing room as well so I can't state any sort of preference for that. But you want to be in the latter stages of competitions. He has played in a Champions League Final with Tottenham, he has now got a second League Cup Final coming up and for certain, those are the occasions as players you want to be involved in.
"You want to be involved in the major tournaments and you want to be in the important matches, domestic cups and the league of course."
"He didn't warm up with the rest of the team but he did the rest of the session after so he should be fine," added Southgate, who is aiming to secure three wins from England's opening three Group I games following wins against San Marino and Albania.