Zinedine Zidane's search for a long-term replacement for Iker Casillas continues, despite the Spaniard having left the Bernabeu a year ago, with Keylor Navas putting in some impressive performances between the sticks last season.
Madrid will be buoyed by the fact that Lloris is yet to sign a contract extension at Spurs, though he still has three years left to run on his current deal.
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Spurs' main man
Tottenham boss Mauricio Pochettino is keen to keep his stopper at the club, so the Lilywhites would surely fight hard to hold onto the 29-year-old were Madrid to make a concrete offer.
The French captain has been at Spurs for four years, having signed from Lyon in a £10million deal.
Last season, Spurs boasted the joint-best defence in the Premier League thanks in large part to Lloris, so it's clear how he has caught Madrid's eye.
Now that Madrid have confirmed they will not be making an offer for Manchester United goalkeeper David de Gea, their attentions have clearly turned elsewhere, but Spurs fans need not panic just yet.
According to ESPN, Zidane is not ready to launch an all-out offensive to bring in a goalkeeper, as he would personally be happy to keep Navas, especially after winning the Champions League.
If the club's hierarchy want to bring in a big name, however, Lloris fits the bill perfectly, having proven himself at the highest level time and again with France.
And if Les Bleus continue in the form they have been in, he could even be heading to the Spanish capital with a European Championships medal.
How would Spurs do without Hugo Lloris? Have your say in the comments.