Manchester City wanted to sign Kane in the summer, but saw their approaches consistently rejected despite the player making clear his desire to leave.
Kane remained, but struggled to reach top form for the club at the start of the season, however, recent performances have shown improvement with three goals in his last three league games under new manager Antonio Conte.
And it is thought the rearranged structure in north London could have impacted the player's mindset.
Speaking on talkSPORT Drive on Wednesday, Bent - who played for Tottenham between 2007-2009 - mentioned a promising rumour for the club, which would be good news for fans.
Bent said on talkSPORT Drive: "I heard - and I have to stress it was a rumour - but it's that he's potentially going to stay and sign a new contract there.
"And you start thinking, 'Well, what are Manchester City gonna do now?'
"They've let Ferran Torres go and you think, 'That's a bit strange because they've not got no centre forwards now.'
"Are they making room for Erling Haaland? And that's potentially why he could stay and sign a new contract?
"This is what I'm hearing, but as I said, I'm doing a full [talkSPORT transfer journalist] Alex Crook here with the rumour, the speculation.
"For Spurs fans, that'd be fantastic, but does that mean that maybe Manchester City are going down the younger route? Maybe a Haaland?"
Haaland has been regularly linked with City - as well as many top clubs in Europe.
The Borussia Dortmund striker is still just 21 years of age and flourishing at the Bundesliga side.
However, many speculate that he could be set for a move elsewhere in the not-too-distant future.