The 23-year-old has attracted plenty of admirers as Leeds' number one and is being tipped to make the switch to a European-chasing club in the upcoming transfer window.
Despite Meslier's best efforts, Leeds are involved in a nine-team relegation dogfight at present, sitting 16th in the Premier League table with 29 points from 30 games this season.
Javi Gracia's side are only two points clear of the drop zone with eight matches left to play, and Meslier has just five clean sheets to his name, shipping 54 goals in the top-flight campaign.
Only Bournemouth (57) have a worse defensive record in the current Premier League season, while Nottingham Forest have also been breached 54 times, but Meslier will not be short of offers this summer either way.
Should Leeds fail to stay in the Premier League, the consensus is that Meslier will be on his way out to continue in the top flight, as well as a number of other Whites players.
However, Football Insider claims that the Frenchman is planning to depart even if Leeds avoid the drop, and Chelsea have shown the most serious interest in his services throughout the campaign.
The report states that Frank Lampard's side are "very keen" to bring Meslier to Stamford Bridge this summer, and they are ahead of Manchester United and Tottenham Hotspur in the race for the 23-year-old.
Meslier is under contract at Elland Road until the end of the 2025-26 season, and Leeds are expected to demand at least £40m to sanction a sale in the upcoming window.
The France Under-21 international spent 11 years on the books at Lorient, the last of which saw him loaned out to Leeds during their triumphant 2019-20 Championship campaign.
Upon his arrival at Elland Road, Meslier played second fiddle to Kiko Casilla, but he made his breakthrough in the final few weeks of the 2019-20 season after Casilla was banned for eight games for racially abusing Jonathan Leko.
Meslier retained the number one spot upon Leeds' promotion to the top flight and has now made 122 appearances for the Whites in all tournaments, recording 30 clean sheets in the process.
Chelsea currently have Edouard Mendy and Kepa Arrizabalaga battling for supremacy in West London, while Marcus Bettinelli and the up-and-coming Gabriel Slonina provide backup to the duo.
Kepa has wrestled the gloves out of Mendy's grasp this season, but both shot-stoppers are facing uncertain futures at Stamford Bridge as the Blues search for a new number one.
Lampard's men occupy 11th place in the Premier League table ahead of Saturday's showdown with European contenders Brighton & Hove Albion at Stamford Bridge.