PSG have been seen as one of the frontrunners to land Messi's signature in recent weeks, but Tuchel has downplayed his side's chances of landing the six-time Ballon d'Or winner.
The German tactician was speaking after his side's narrow 1-0 loss to Bayern Munich in Sunday's Champions League final when he revealed that, while he would have to invest in his squad for next season, Messi was an unlikely acquisition.