The France international has missed two days training with a throat infection and has taken a test to see if he is COVID-19 positive, according to L'Equipe.
The French World Cup star missed team training Monday and Tuesday and was reported to have a sore throat, with his club needing to overturn a 2-1 deficit from their first-leg defeat in Germany two weeks ago.
Mbappe has scored six goals in his last three PSG matches.
At Monday's training session Argentine forward Angel Di Maria was observed passing the ball around with Neymar. Spanish forward Pablo Sarabia is also a likely inclusion should Mbappe miss the game.
PSG lost 2-1 to an Erling Haaland-inspired Dortmund before a crowd of 80,000 in Germany last month, with the return-leg to be played in an empty Parc des Prices stadium due to the coronavirus.
Instead, according to Paris Saint-Germain boss Thomas Tuchel, the World Cup winner is suffering from a bout of angina.
"Kylian is sick," said Tuchel. "He was sick yesterday and he is sick today with angina and we are trying to maybe have a light practice (with him) this evening."
Angina can reduce the flow of blood to the heart, but Tuchel is hopeful of having Mbappe in his team for the must-win Champions League last-16 clash with Dortmund, who they trial by two goals to one from the first leg.
"He did not practice with us the last two days," added the PSG boss. "We must wait and decide tomorrow morning (whether he will play)."
Paris Saint-Germain's task of winning the tie has been made harder after it was confirmed that the match at the Parc des Princes will be played behind closed doors.
The decision was made by Paris police on Monday to help contain the spread of coronavirus.
PSG responded by the news by confirming the club is "fully mobilised" to ensure the match goes ahead in the "best possible conditions".
Meanwhile, Paris Saint-Germain manager Tuchel added: "It's another strange situation because we're playing without our spectators.
"In a match of this importance, they are very important to create a special atmosphere, tension, pressure on our opponent. With what's happening between coronavirus and Kylian Mbappe's illness, we have to adapt and think.
"Kylian has a sore throat and we'll see if he can train a bit on Tuesday evening, but he hasn't been with us for two days. We'll wait and see and decide on Wednesday morning."