The 23-year-old has impressed for the Whites since making the switch from French club Lorient in August 2019, appearing in 128 matches for the Yorkshire-based side across Premier League and second-tier campaigns.
Meslier turned out on 34 occasions for Leeds in the top flight last term as they were relegated to the Championship, with United conceding a division-high tally of 78 goals in 38 matches.
The keeper has respectable international pedigree having played 11 times for France Under-21s since making his debut in October 2019, however the youngster is yet to receive a senior call-up for Les Bleus.
According to Sport, Real Madrid are weighing up a move for Leeds stopper Meslier this summer, following the injury picked up by first-choice goalkeeper Courtois.
The Belgium international has sustained a serious ACL injury during Los Blancos' pre-season preparations this month, and the former Chelsea man could miss the entirety of the 2023-24 campaign.
It is therefore understood that Carlo Ancelotti is keen on recruiting a top-quality goalkeeper to replace the sidelined Courtois in the coming months, and Leeds stopper Meslier is said to be of interest.
The Frenchman was part of the Leeds team which drew with Cardiff City at Elland Road on the opening day of their Championship campaign on Sunday afternoon, as the hosts came back from two goals behind to force a share of the spoils.
Meslier is supposedly not the only keeper that Real have their eyes on, with Sevilla man Yassine Bounou reportedly pressuring his club to allow his sale to the Spanish giants, according to MARCA.
The separate report claims that discussions are underway over a potential switch between the two La Liga outfits, with Los Blancos said to be favouring the capture of the 32-year-old over any other player at this moment.
Real are said to prefer a deal for the Moroccan due to his similar stature and attributes to Courtois, although they are concerned that he would be away at the Africa Cup of Nations for a month at the start of 2024.
It is believed that Sevilla are looking to pocket €30m (£25.8m) from the sale of Bounou - a player who has featured 140 times for Los Nervionenses since joining from Girona in September 2019.
Despite transfer speculation, Meslier is expected to be in between the sticks for Leeds at St Andrew's tomorrow, when Daniel Farke's side face Birmingham City in the Championship.
Real Madrid look set to begin their La Liga title challenge without an established first-choice keeper this weekend, as Ancelotti's men make the trip to Athletic Bilbao on Saturday.