However, Manchester United and Chelsea are two clubs who are said to be interested in the player and should Spurs fail to win major silverware over the coming years, he may just be tempted to move. Our live coverage lets you follow all the key moments as they happen.
Tottenham manager Mauricio Pochettino said when asked about his player's agent situation: "His big issue must be to focus on trying to improve and develop his game, to stop and try to be better every day". Find out by following our live matchcast. Last week, Tottenham defeated Everton 3-0 and Borussia Dortmund 3-1 in Champions League on Wednesday.
The contrast is all the more dramatic given Spurs' relentless form at White Hart Lane last season, where they were unbeaten in the league and took 18 points out of 18 against the league's bottom six.
Lots of people connected with Tottenham Hotspur had bad days, but the one person who came out of Saturday's 0-0 draw with Swansea looking the worst was probably match official Mike Dean. Kane has won the Premier League Golden Boot two seasons in a row, while Pochettino has guided Spurs to consecutive top-three finishes.
Pochettino was particularly disappointed with referee Mike Dean's decision not to award Aurier the foul.
Pochettino criticizes Mike Dean over missed Tottenham penalty call
"For me that goal was an incredible goal because it meant for us, for everyone, the possibility to stay here today", he said.
The Wales worldwide defender played in Spurs' 3-1 Champions League win over Borussia Dortmund - their first win in five matches at their temporary home.
Today, Spurs will be played without Victor Wanyama, Danny Rose, and Erik Lamela. "We can not compare last season with this season". I never like to speak about the referee.
The England Under-21 worldwide had looked to have made a complete recovery and has featured off the bench three times this season, but Pochettino says there are still lingering concerns.
"I thought we defended very well and we had to, we had to defend very well".
Oh mother! ... Jennifer Lawrence film receives F CinemaScore
They are actually getting less and less as I get older, which is starting to worry me. Seems like American actress Jennifer Lawrence is in no hurry to be a "mommy".