Messi is expected to end his long association with the Spanish giants when his current contract expires at the end of this season, having reluctantly been made to stay at the club after pushing for an exit this summer.
The six-time Ballon d'Or winner has openly criticised the club's board and will not open talks over an extension with the current hierarchy in place, leaving Manchester City as front-runners for his signature.
Marca reports that Barcelona have now earmarked Mbappe as a possible replacement for Messi, with recent reports suggesting that the 21-year-old has no intention of extending his PSG contract beyond 2022.
PSG could therefore look to cash in on Mbappe next summer, although his €200m (£182.9m) asking price could prove problematic for a Barcelona side struggling financially in the wake of the coronavirus pandemic.
Some reports have suggested that the World Cup winner could be available for as little as £91m, though, leading to interest from a number of Europe's biggest clubs.
Real Madrid are thought to be leading the race for his signature, while Liverpool and Juventus have also been linked, with the latter reportedly lining up a blockbuster swap deal between Mbappe and Cristiano Ronaldo.
Mbappe has scored 94 goals and set up 55 more in 128 games for PSG.