The France striker was declared fit for Tuesday's Champions League last-16 first leg at the Parc des Princes after taking part in two training sessions.
Mbappe had initially been ruled out for three weeks with a hamstring injury he sustained on 1 February, but he was on the pitch with his teammates on Sunday and again on Monday.
Coach Christophe Galtier had said on Saturday that he would take 'zero risk' with Mbappe and on Monday he said he would make a late decision.
"He's done everything possible to make himself available for this match," Galtier said.
"We'll see tomorrow morning how he feels. The first person I'll listen to will be Kylian, then I'll make the wisest decision."
Lionel Messi and influential midfielder Marco Verratti are also back from injury.
PSG have been in poor form recently, losing 3-1 at Monaco in Ligue 1 on Saturday – their fourth defeat of the year in all competitions.
Bayern's Thomas Muller also trained on Monday, suggesting he will be available after coming off at half-time in Saturday's 3-0 win over Bochum as a precaution.
But the German champions will be without long-term absentees Manuel Neuer, Lucas Hernandez und Sadio Mane.
In the night's other game, AC Milan host Tottenham.
Spurs' Italian coach, Antonio Conte – a former Juventus and Inter Milan manager – has won eight of his last nine games against Milan in a run dating back to 2013.
But Spurs have lost Uruguayan midfielder Rodrigo Bentancur for the season with a ruptured anterior cruciate ligament while Pierre-Emile Hojbjerg is suspended, so Conte is likely to turn to the inexperienced Oliver Skipp and Pape Matar Sarr.
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