The 19-year-old is set to join the Whites on a season-long loan from French second tier side FC Lorient, if he passes his medical.
Meslier played 30 games for Lorient last season, 28 of them in the league and he kept 11 clean sheets.
But the 6ft 4ins stopper has been on the bench for the first two Ligue 2 games of the season.
Meslier has been tracked by Chelsea and has previously been a target for Monaco.
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The Whites currently have four loanees, in Ben White, Helder Costa, Jack Harrison and Jack Clarke.
Only five are permitted in a matchday squad, but international loan signings can be classed as permanent players and don't count towards that total.
Meslier's arrival doesn't rule out the possibility of a further loan arrival before tomorrow's deadline.