Danny Murphy has said that even if United have to shell out a club-record fee for the 26-year-old, it would be worth it as a top-class forward is the "final piece in the jigsaw" for the club.
Kane recently indicated he could be eyeing the exit door at Spurs, saying he could leave if the club do not progress a sufficient amount.
That news would likely have been of interest to United, who have long had their eye on the England international.
Murphy has said that money should not be an object in United's pursuit of Kane, such would be the importance of his signing for the Old Trafford side.
"The final piece in the jigsaw is a world-class centre-forward. We know it and they know it. It is why they tried to sign Erling Haaland in January.
"If Harry Kane is available, even for a record price, United would be mad not to look a gift horse in the mouth."
Breaking the club's record fee would mean Man Utd would pay more than the £89.3 million ($111m) they shelled out for Paul Pogba in August 2016.
With Spurs chairman Daniel Levy known as a tough negotiator, it would likely take a nine-figure offer to convince him to sell to a Premier League rival. Some reports have even quoted a price as high as £200m ($249m).
Even if the the figure climbs that high, Murphy insists that a club a rich as United have an obligation to spend on a player that can be a difference-maker.
"They are the richest club in England," Murphy said of Ole Gunnar Solskjaer's men. "If there is ever a time to use that financial power, it would be to prise the best striker in the country away from Tottenham.
"If United have the money, they should spend it on Kane. He can turn them from a team with potential, into genuine challengers."