Since moving to Leeds in 2019, Meslier has established himself as the first-choice stopper at Elland Road, making 126 appearances in all competitions.
However, despite possessing a contract until 2026, the perception is that the 23-year-old will leave this summer courtesy of the club's relegation from the Premier League.
That is despite the Frenchman's stock dropping during the second half of the season, caretaker boss Sam Allardyce choosing to drop him from the starting lineup.
Nevertheless, a number of top clubs around Europe may look to take advantage of the situation, aware that they would be signing a young goalkeeper with potential resale value who has made over 100 appearances in the Premier League.
Chelsea are known to be in the market for a new stopper this summer with at least one of Kepa Arrizabalaga or Edouard Mendy expected to leave Stamford Bridge.
As it stands, the likes of Inter Milan's Andre Onana and AC Milan's Mike Maignan are seemingly towards the top of Chelsea's shortlist, but a move for Meslier cannot be ruled out.
That said, Meslier has made it clear that he would not necessarily accept an offer to move to Chelsea, insisting that he will not sign for the Blues to become second choice.
Speaking to RMC Sport, Meslier said: "For now, I have a contract until 2026. Officially, I still belong to Leeds. I will have to think about what could be the best project, be that at Leeds or another club.
"If it is to go and be on the bench, I'm not interested in that. If it's to be the number one, of course, you can't say 'I'm not interested in Chelsea.'
"I'd prefer to go to a less reputable club where I'll have more game time than a top European club where I'd sit on the bench."
Chelsea also have young American stopper Gabriel Slonina on their books, although he is not expected to be considered as a potential number one until at least 2024-25.
Meanwhile, Leeds may not make any decision over the future of Meslier until they have appointed a new manager, just days after it was revealed that the club's ownership would be changing hands.