TheSunclaim a deal could be done for around £40million as United look for a long-term successor to Wayne Rooney.
Kane, 21, is seen as the ideal understudy to Rooney, 30, as the Red Devils want an English figurehead to lead the line for years to come.
The report suggests Spurs might be willing to do business if they receive a "dizzying" offer for their young star and United are desperate for striking reinforcements.
The decision not to make Radamel Falcao's loan move permanent has left a void at Old Trafford.
United boss Louis van Gaal has grown increasingly frustrated at failing to land his top summer transfer targets, with numerous forward options seemingly going by the wayside.
GETTY
Harry Kane is reported to be a top target for Manchester United
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
The Red Devils had been linked with a move for Mario Mandzukic but the Croatia forward joined Juventus.
Colombia striker Carlos Bacca has also eluded the Dutchman after signing for AC Milan.
United face a battle to sign Kane, with the North London club keen to keep hold of one of their prized assets.
In a bid to stave off prying eyes from Manchester, Spurs are reportedly keen to make him captain and tie him down to the club.
But United could make it a double raid as they are also reported to be weighing up a move for French stopper Hugo Lloris.
With David de Gea strongly linked with a move to Real Madrid, the 28-year-old could join Kane at Old Trafford and slot straight in as first-choice goalkeeper.
Tottenham insist they are not in talks with United and maintain they have no interest in selling Kane.