According to MailOnline's Amitai Winehouse, Pochettino said of the striker's long-term future:
"That is a question for him, not me. Of course, he wants to score goals and win titles but I cannot say anything more about this.
"He is so happy here and he loves Tottenham, but this is a personal question, regarding what he thinks and how he feels. I cannot answer for him."
It's to be expected the 24-year-old is on the radar of Europe's elite given his exploits for the Lilywhites in recent years.
The forward netted his 100th Premier League goal against Liverpool last Sunday and became the second-fastest player to reach that tally, per OptaJoe:
100 - @OptaJoe takes a look at how @SpursOfficial striker @HKane scored his 100 @PremierLeague goals & how quickly he reached the tally compared to previous leading strikers. Superstar. https://t.co/c2nb9Nw90r2018-2-5 13:43:59
Kane has spearheaded an impressive rise at Spurs under Pochettino, but while they've developed into title challengers in recent years, they have no silverware to show for their efforts.
Sky Sports MNF @SkySportsMNF
WATCH: "His motivation is going to change from goals to trophies." Wayne Rooney warns Tottenham could lose Harry Kane if they don't match his ambition soon. See Rooney on MNF on Sky Sports PL now or follow what he says here: https://t.co/U9av7f4CWv https://t.co/yr4UMJmrmx2018-2-5 19:45:00
Kane has discussed his ambition to win titles:
B/R Football @brfootball
Harry Kane has the motive 🏆 https://t.co/VQQWBp7FJH2018-2-5 12:32:00
While the striker evidently hopes to achieve that with Spurs, and he can cement his status there if he stays put, the lure of a club like Real Madrid and the trophies they can offer could well grow the longer Spurs go without winning something.
A player of Kane's calibre should be challenging for major honours every season, so it would not be too surprising if he were to follow in the footsteps of former Tottenham hero Gareth Bale and move to the Santiago Bernabeu.
Kane has a stronger connection to the club than Bale did, though, and Spurs will hope that's enough if they're unable to meet his ambition for trophies.