Kane pushed to join Manchester City last summer and is thought to have rejected a contract extension shortly after reluctantly conceding that he would be staying at Spurs.
But the England captain is now said to be excited by Spurs' progress under Antonio Conte and increasingly hopeful he can fulfil his ambitions of winning a trophy with his boyhood club next season.
Kane is yet to hold talks with the club, with two years to run on his current deal, and has been focussed on securing Champions League qualification.
The striker is also waiting to discover the outcome of Conte's crunch talks with managing director Fabio Paratici this week but, provided Spurs back the head coach as planned, Kane is thought to be happy to entertain an approach from the club when he returns for pre-season.
Kane turns 29 in July and signing a fourth long-term deal since his breakthrough would boost his chances of spending his entire career at Spurs, and surely see him comfortably break Jimmy Greaves' all-time scoring record for the club. He has also set his sights on Alan Shearer's Premier League record and finished the season with 17 top-flight goals, despite having just one when Conte arrived on November 2.
Kane is currently in New York - where he is due on Thursday to appear on 'The Tonight Show Starring Jimmy Fallon' - and will join up with England for next month's UEFA Nations League quadruple-header before a short holiday.
Kane has been more settled at Spurs since Conte's appointment but was said to remain undecided about their prospects earlier this year. He has been hugely encouraged by their return to the Champions League after a two-year absence and the club's plans to revamp the squad this summer.
Spurs announced a £150million injection from owners ENIC on Tuesday, with Conte set to be handed the majority to spend on new players - provided he is happy to stay.