Mbaye, an 18-year-old right winger, starred for Senegal at the World Cup and was earlier made available to a number of clubs, with Manchester City and Tottenham understood to have shown greater interest at that stage.
Bundesliga side Bayer Leverkusen have since made the most progress in talks, though Liverpool are now weighing a move themselves amid concerns about their squad's firepower following Mohamed Salah's departure to Trabzonspor.
Mbaye would represent a more natural fit as a replacement for Salah than Barcola, who prefers to operate on the left, though much will depend on PSG's asking price, which is likely to be north of £150m for the pair combined. The clubs are expected to maintain dialogue over the coming days as the situation becomes clearer.
Mbaye, who is represented by agent Jorge Mendes, has been at PSG since 2018 and has made 33 appearances for the senior side, scoring four times. He represented France at youth level before switching his international allegiance to Senegal in 2025, and became the youngest African scorer in World Cup history when he netted a consolation goal against France at this summer's tournament in the United States.
The 6ft 1in winger's rapid rise has made him one of the more sought-after teenage talents in Europe this summer, with suitors across England, Germany and beyond monitoring his situation as PSG weigh up player sales following a busy summer of their own recruitment.
Liverpool's interest in the pair reflects the scale of the rebuild facing Andoni Iraola following Mohamed Salah's exit, with the Spaniard yet to settle on a long-term right-wing solution since taking over at Anfield.
Barcola, who prefers the left flank, would address a different problem, with Liverpool having long been linked with the France international as they look to add depth and competition across their forward line.
Should Liverpool move for both players, it would represent one of the more ambitious swoops on a single rival's squad in recent transfer windows, though PSG's valuation of well over £150m combined is likely to test Liverpool's resolve as the market continues to shift in the closing weeks before deadline day.