The England international has been heavily linked with a move away from Spurs in the summer with his contract to expire in 2024.
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There is no indication yet on whether the 29-year-old will extend his stay, with the Red Devils understood to be circling the striker.
It was revealed earlier in the week how United were laying the groundwork to secure his services.
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And it has also been claimed Erik ten Hag's side are willing to offer him a huge pay rise to increase his salary from £200k-a-week to £300k-per-week.
United fans have clearly given the club their seal of approval to make a move for Kane after singing about the Three Lions forward during the first half.
With the visitors in cruise control in the capital, supporters sung in unison: "Harry Kane, we'll see you in June."
Meanwhile Red Devils legend Rio Ferdinand urged his former employers to bring the player to Old Trafford.
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The BT Sport pundit said: "If there aren't conversations going on in the corridors of power about Kane then I'd be surprised."
He then quipped: 'Sell now before the season even finishes. Manchester United have to be looking at the turmoil that Tottenham are in."
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Despite United fans mocking the Spurs supporters, they came together in the first half in wanting to get rid of their owners as they sang chants against their respective board.
Tottenham fans were furious going into the match as they vented their anger towards owners ENIC and chairman Daniel Levy after protesting against the board.
And they continued to have their voices heard inside the stadium as they sang: "We want Levy out."
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United supporters meanwhile chanted: "We want Glazers out."
It was another first half to forget for the hosts, as just like in their 6-1 drubbing away at Newcastle, they were outfought and outclassed.
Though thankfully for new caretaker boss Ryan Mason, Spurs didn't go into the break 5-0 down.
Instead they trailed by just two goals, with Kane's England teammates Jadon Sancho and Marcus Rashford grabbing the goals.
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And just like Spurs earlier in the season, they were a different team in the second half as they showed their fighting spirit to earn a point.
Goals from Pedro Porro and Heung-min Son have seen Tottenham move up into fifth spot, though they still trail United by six points.