The England international recently admitted to being in the best form of his life after netting 15 goals in his last 10 appearances for club and country.
According to The Sun, however, Spurs now face competition from closer to home as United are prepared to spend big in their pursuit of the prolific centre-forward.
The report suggests that the Red Devils will up Kane's wages, which could rise to £140,000 should he sign a new contract in the meantime, having initially missed out on the 24-year-old in 2015.
A United source is quoted as saying: "The club had asked about Kane's availability a few years back. They were told by Spurs there was no chance. Jose is a big fan and is very interested.
"Zlatan Ibrahimovic will move on next summer, more than likely, freeing up a load of cash they plan to use. The problem for United is the money could get to a ridiculous level.
"It's going to be more than Kylian Mbappe. It's money they can lay their hands on but it will be interesting to see what [Daniel] Levy's stance on the whole thing will be."
Overall, Kane has scored 84 goals in 120 Premier League games for Spurs since being handed his debut in 2009.