The England skipper was kept quiet by Victor Lindelof and Harry Maguire as United came from behind to dent Spurs’ top four hopes with a 3-1 win in north London on Sunday.
Kane refused to commit his future to the club during the last international break and reports over the weekend claimed the 27-year-old will request to leave the club if they finish outside the top four.
Spurs’ defeat means they’re six points short of West Ham, who currently occupy the final spot in the top four.
United are keen on signing Kane and are willing to explore the transfer, despite recnognising how difficult it will be to prise the forward away from the capital.
And Keane believes that Kane is keen on moving to Old Trafford, particularly as it means playing with the likes of Paul Pogba and Bruno Fernandes.
‘For Kane he’d be looking at this United team today and listen they’ve made progress over the last 12 months and surely Kane must be thinking: ‘I could be the top man at Manchester United up front y’know?’ said Keane.
‘With the service he’d be getting, Kane must fancy United.
‘I think Kane fancies United, I just have that feeling that he fancies United. Just a gut feeling.’
Kane’s desire to leave Spurs as because of his desperation to win silverware.
United last won a trophy in 2017, when Jose Mourinho guided them to victories in the Carabao Cup and Europa League.
Manchester City are also interested in Kane and would provide a greater certainty of silverware but Keane believes trophies would come at Old Trafford if Kane joins.
‘If Kane is in the United team, as night follows days yeah,’ said Keane.
‘Manchester United have closed the gap on City and Kane would be another huge step. Maybe Kane doesn’t want to go abroad, Manchester United are still a huge, huge pull.’