He is trying to sign players this month, with Dele Alli potentially on his radar, but he is also looking long-term and is keen on a reunion with Lloris in the summer.
He views the France captain as an upgrade on Keylor Navas and thinks he can pick him up for a good price given he only has a year left on his current deal.
Mourinho is weighing up potential replacements and views Henderson as a good option, according to The Sun.
Henderson has grown frustrated at Old Trafford this season as he remains in David de Gea’s shadow and is keen to secure regular first-team football.
Spurs would offer him that, should Lloris leave and United may be forced to reluctantly part ways with Henderson.
Sam Johnstone, another former Manchester United goalkeeper, has emerged as another option for Spurs.
Lloris, 34, has been a consistent performer in north London since joining from Lyon in 2012 but Spurs’s hierarchy fear he will move on.