Clarence Seedorf's hopes of guiding Milan to European football look all but lost after they were beaten 2-1 by Atalanta last time out.
Franco Brienza scored deep into injury time on Sunday to snatch three points for the hosts and deal Milan a major blow in their quest for Europe.
Milan must now beat 16th-placed Sassuolo and will likely need both Torino and Parma to lose on the final day of the Serie A campaign - they take on Fiorentina and Livorno respectively.
Their season finale comes amid strong rumours that Seedorf, appointed as Massimiliano Allegri's replacement in January, will be sacked in the close-season despite making a reasonably positive start to his managerial career.
Even qualification for Europe's second-tier club competition is unlikely to do much to strengthen his position but the Dutchman is eager to finish the campaign on a high - whether it proved to be his final match in charge or not.
"We'll be hoping to do well in the last match," he said after the defeat to Atalanta.
"There's some disappointment for the loss and for how we lost. Now we have to wait and see. Our destiny wasn't completely in our hands even before and it's less so now."
Midfielder Kaka added: "We need to win next Sunday for our pride and to close the season well."
While the pressure is on Milan going into their final game of the season, Sassuolo can relax knowing they have already secured their top-flight status.
Eusebio Di Francesco has helped the club to Serie A safety after their first season in the league, having taken 10 points from their last five games, and will look for a repeat of their dramatic 4-3 win over Milan early this year.
If this does prove to be Seedorf's final game in charge, there would be a certain symmetry to it all, as the seven-goal thriller in January was the final straw for Milan in Allegri's reign.
Domenico Berardi scored four times that day at the Stadio Citta del Tricolore and, even if they fail to do the double over Milan, Di Francesco feels their season has already been a success.
"This safety is worth a Scudetto for us, so achieving it a round early is nothing short of miraculous," he said.
Seedorf has no fresh injury concerns and could hand a debut to 15-year-old Hachim Mastour. Should he play, he would edge out Paolo Maldini to become the youngest player to feature for the club.
