Lloris is looking for Champions League football and has told Spurs of his intention to leave the club if they do not qualify for the competition.
Meanwhile, Man United have made initial contact with the Frenchman over a move as they await developments in the De Gea situation.
United remain hopeful of keeping De Gea but his continued reluctance to sign a new deal at Old Trafford has forced the club to search for contingency plans.
De Gea is among the best goalkeepers in the world and would be virtually irreplaceable should he leave.
The Spaniard would be a big miss but Lloris is a quality player and would go a long way towards filling the void.
However, Spurs chairman Daniel Levy may not be so happy with the situation and will likely fight tooth and nail in getting the best price for the player. As the Gareth Bale saga showed, Levy is notoriously difficult to negotiate with.