Mbaye broke through at PSG last season, scoring three goals and providing two assists in 24 league appearances, ten of them starts.
The 18-year-old Senegal international has two years left on his contract, but looks set to leave the French champions this summer regardless.
Manchester United, Bayern Munich, Bayer Leverkusen and Borussia Dortmund are among the clubs to have been credited with interest, but it is Liverpool who have moved decisively.
According to RMC Sport, the English club have agreed a five-year contract with the teenager, who has decided to snub Bayer Leverkusen's interest in favour of a move to Merseyside.
Liverpool are hoping to complete a double deal, with the club also chasing Mbaye's PSG teammate Bradley Barcola, long viewed as the priority target in their search for a new winger.
Liverpool plan to continue negotiations with PSG over both players, though there is currently no agreement in place between the two clubs.
Earlier reports had already suggested Liverpool were closing in on a separate agreement with Barcola himself. The 23-year-old has two years remaining on his own contract and has made clear he has no intention of extending his stay in Paris, adding further weight to Liverpool's hopes of completing what would be a significant double swoop on PSG's attack before the transfer window closes.
Mbaye's rise at PSG has been rapid, having broken into the first-team picture only over the past year after progressing through the club's youth ranks. His versatility across the front line, capable of playing on either wing, has made him a player of considerable interest across Europe despite his tender age, with PSG head coach Luis Enrique having recently signalled the club's willingness to move on players who no longer appear fully committed to the project in Paris.
Both Mbaye and Barcola were notably left out of PSG's squad for their French Super Cup defeat to Lens, a decision widely read as a sign that their exits are now considered a formality.