Lingard, 27, is surplus to requirements at Old Trafford after a poor campaign last term.
The midfielder scored just once in the Premier League and he admitted that off-field difficulties had contributed to his poor form on the pitch.
Lingard’s best season came in the 2017/18 campaign under Mourinho at the Theatre of Dreams, where he managed 13 goals in all competitions.
Ole Gunnar Solskjaer is keen on signing Jadon Sancho but the club are struggling to meet Dortmund’s £108m asking price.
Raising as much as £20m through the sale of Lingard could aid United’s cause and the Times claim that Spurs have held talks with intermediaries over signing the midfielder.
A deal for Lingard could hinge on Dele Alli’s future. The England international was left out of Spurs’ squad for the 5-2 win against Southampton on Sunday, which is the second squad in a row in which he was omitted.
Alli has been offered to the likes of Real Madrid and Paris Saint-Germain but Tottenham are struggling to find a buyer for the midfielder.
Nevertheless, the club are keen on recouping some of their outlay through the sale of Alli, who was once valued at around £100m by the club when Mauricio Pochettino was at the helm.