The Sun says Mourinho is eyeing a record £170m swoop for Kane.
The Red Devils sounded out Spurs two years ago over a possible £40m deal which included Javier Hernandez.
Mourinho has been a long-term admirer of the in-form England striker, and is keen to bring him to Old Trafford.
He believes a potential partnership with Romelu Lukaku could turn United into a dominant European force again.
Spurs are adamant they will reject ANY approaches for their star players, especially Kane.
An Old Trafford source said: “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."