Pablo Sarabia scored from two Mbappe crosses and Senou Coulibaly scored another own goal in a thumping finale.
"I can feel he's there", said Tuchel.
But he seized his opportunity, sprinting down the wing and hitting a firm cross toward striker Edinson Cavani that was turned into his own net by Dijon defender Wesley Lautoa.
"I don't know - we will discuss and decide on Friday, as late as possible if he can play on Saturday against Amiens".
It was the second remarkable own goal in a week to be scored for PSG, who also saw Lyon's Fernando Marcal slam a stunning effort past his own goalkeeper at the weekend.
However the hosts were level in the 13th minute thanks to a impressive low curling effort from Mounir Chouiar, which squeezed past Kaylor Navas. We can not risk his health.
League leaders PSG illustrated the gulf in class towards the end of the first half as Kylian Mbappe restored their advantage, and defender Thiago Silva struck a third five minutes into the second half.
The 28-year-old Neymar, who joined PSG in 2017 for €222 millions (US$250 million at the time) missed last season's defeat to Manchester United at the same stage of the Champions League with a foot injury.
Rennes, which beat PSG in last year's final, advanced on Tuesday. We produced a very strong performance.
Later, Lyon coach Rudi Garcia knocked his former side Marseille out as Houssem Aouar scored an 81st minute victor.
In Thursday's remaining quarterfinal, struggling first-division side Saint-Etienne travels to fourth-tier Epinal, which knocked out Lille in the previous round.