The Portuguese manager is expected to be named as Louis van Gaal's successor at the Theatre of Dreams imminently (Sky Sports).
Lloris, 29, joined Spurs in 2012 and has since established himself as one of Tottenham's most consistent performers.
Not only will manager Mauricio Pochettino be desperate to keep him, but the Frenchman would most likely shun a switch to Old Trafford - if Mourinho does indeed want him.
As mentioned, there are few better goalkeepers in world football than De Gea and the former Lyon ace would know that his first-team prospects would be severely limited - in Premier League action, at least.
On the other hand, Mourinho might well be anticipating renewed interest from Real Madrid regarding De Gea, who nearly joined the Spanish giants last summer.
Whatever happens, Tottenham would be handsomely compensated should the transfer materialise, with Lloris - whose contract expires in 2019 - still relatively young as far as goalkeepers go.
Tottenham's Hugo Lloris