Earlier reports had linked the Egypt international with a move to the French capital and Salah has been coy about committing his future to Anfield.
Mbappe has emerged as one of the best players of his generation and his performances have seen him linked with several clubs across Europe.
Real Madrid are said to be the forerunners to sign the World Cup winner and Mbappe himself has admitted to the allure of the Spanish giants in the past.
The France international's current deal with PSG will run out in 2022 and talks are currently ongoing to see if it can be extended. However, Neymar's contractual obligations will also put a strain on the club's purse if it is to also be extended.
The current financial climate means that it might be impossible to afford to keep both players.
If Real Madrid do get to sign Mbappe, PSG will have to sign an alternative and have reportedly identified Salah as their top target.
The 28-year-old has continued to perform at a high standard despite Liverpool's struggles this term and is joint-top of the scorer's chart as he chases down a third Premier League Golden Boot.
Salah was again on the scoresheet to spark Liverpool's 2-1 comeback victory against Aston Villa, while he also netted the sole away goal in the 3-1 defeat to Real Madrid.
Kylian Mbappe leading PSG's charge for a semifinal appearance in the UEFA Champions League
PSG's pairing with Bayern Munich in the quarterfinals of the UEFA Champions League was a rematch of last season's final.
A lot has changed since that August night in Lisbon, chief of which was the replacement of Thomas Tuchel by Mauricio Pochettino in the PSG dugout.
The absence of red-hot Robert Lewandowski due to a knee injury is also a key difference but nevertheless, both sides still have enough quality players in their ranks to make a difference.
Kylian Mbappe stood up to be counted for PSG. Fresh from his four-goal haul against Barcelona in the last round, the 22-year-old once again upped the ante by starring with a brace in Munich.
This propelled the Parisians to a 3-2 away win and firmly put them in the driving seat ahead of the return leg this week.
PSG uncharacteristically find themselves playing catch-up at this stage in Ligue 1 but with European glory firmly within reach, the season could end at an all-time high.