The 25-year-old has established himself as one of the Premier League’s chief performers in recent years and won the Golden Boot following his exploits at the World Cup back in the summer.
Manchester United have always tried to poach the biggest talents English football has to offer. Their deal for Wayne Rooney in 2004 was proof of that.
And the Evening Standard say Woodward would love to lure Kane away from Tottenham and to Old Trafford.
United’s No 9 role is currently occupied by Marcus Rashford.
Rashford has won a place in Ole Gunnar Solskjaer’s team with recent goals against Cardiff, Bournemouth and Newcastle.
Romelu Lukaku, meanwhile, has been stuck on the bench.
United also have Anthony Martial capable of playing in a central position.
But, despite that, the Evening Standard say Woodward would still love to secure Kane’s signing.
However, he has supposedly predicted that Tottenham would make any transfer tricky.
The two clubs have a strained relationship in the transfer market – something that dates back to 2008.
Back then, United controversially poached Dimitar Berbatov.
The Red Devils had flirted with the Bulgarian all summer long but, in a stunning twist, he looked Manchester City-bound.
But United forced Tottenham into letting Berbatov go – much to the ire of Daniel Levy.
And Levy has refused to sell the likes of Luka Modric, Gareth Bale and Eric Dier to United in the time since.
That means, though, that Kane too would be a complicated transfer.
And Woodward is resigned to the fact Spurs would do everything to keep their star man.