Sir Alex Ferguson wanted to land Luka Modric back in the summer transfer window of 2012 – but Levy opted to sell him to Real Madrid instead.
Real Madrid also beat United to the signing of Gareth Bale the following year, despite their Premier League counterparts outbidding them.
Mourinho, while in charge of the Red Devils, eyed deals for Eric Dier and Toby Aldereweireld in 2017 and 2018.
But Tottenham, again, dug their heels in and prevented United from getting a deal over the line.
Kane recently hinted at unhappiness with Tottenham by acknowledging he wants to win the biggest and best trophies on offer.
“Individual awards are great, they are fantastic achievements,” he said.