Kane has long been linked with a move away from Tottenham and could be set to leave the club this winter.
However, Antonio Conte is said to be keen to keep hold of his star forward for the coming season.
Manchester City have registered an interest in Harry Kane ahead of January, reports claim
According to reports from ESPN, new boss Conte was given assurances he could expect to include the England captain in his Spurs plans moving forward.
Kane endured a summer of disappointment after the Three Lions agonisingly lost the Euro 2020 final on a penalty shootout to Italy and his touted mega-money move to City fell through.
As a result, the England captain has seen his form take a hit following a rocky start to the season for club and country, with just one goal in 10 league games so far this term. He was without a goal in his last five matches.
Kane has been linked with a move away from Tottenham and could be set to leave the club
However, Kane, who has had a below-par start to the season with Tottenham, scored a hat-trick to come England’s all-time leading scorer in competitive fixtures with 39, overtaking’s previous record of 37.
Speaking of his performance, Gareth Southgate said: ‘Form is always temporary.
‘What pleased me most was his all round performance because he is always going to score goals, we know that.
‘But he was really on song tonight. I thought Harry gave a brilliant centre forward’s performance – held the ball up, played other people in.
Kane scored a hat-trick to become England’s all-time leading scorer in competitive fixtures
‘But I thought it was very strong team performance. I think we had an edge about us and we are at our best with an edge.
‘We wanted a collective response from the last game (where we drew 1-1 very Hungary) and we’ve spoken about that all week.
‘We addressed that tonight, it’s hard to pick out any individuals.’
Southgate confirmed he will make changes for Monday’s clash in San Marino, but will be without Mason Mount (dental) and Luke Shaw (concussion).
‘We will make a decision on the team, we want to put a performance that is level as it is tonight and finish strongly.’
Kane himself added: ‘Whenever I score I seem to be sharp, whenever I don’t I’m not sharp anymore. That is part and parcel of being a striker. The most important thing is we are moving forward as a team.
‘Great night for the team first and foremost. An important result for us and just the way we went about it. To go 5-0 at half time shows the character of the squad.’