According to Corriere dello Sport (h/t Daily Mirror's Mark Jones), he has six matches to convince Milan of his worth or he will be returning to Stamford Bridge prematurely.
The 24-year-old has barely made an impact in the Italian fashion capital, making two starts in the UEFA Europa League and a further four appearances off the bench in Serie A.
Per Jones, Milan manager Gennaro Gattuso didn't hide how he felt about the midfielder in a recent interview: "Bakayoko has to learn how to get the ball. We must work correctly. It will not be easy. One week is not enough to remove the defects of a player. I would have preferred to be managing older, more experienced club players."
Chelsea paid AS Monaco £40 million for the Frenchman in 2017, but he has been a huge disappointment since making the switch. Fans were amazed at how much better he looked in France:
He's not the first former Monaco midfielder to struggle away from the French club, however, and Milan likely made their move hoping he would emulate Geoffrey Kondogbia. He left for Inter Milan in 2015 and was a complete flop, but has since rediscovered his form with Valencia.
It hasn't worked out that way for Bakayoko, however. Milan have plenty of options in midfield besides the Frenchman, including Lucas Biglia, Giacomo Bonaventura and Franck Kessie. They're also expected to make a play for Zenit Saint Petersburg's Leandro Paredesin January, per Calciomercato.
If the Rossoneri do move for the Argentinian, they will likely sacrifice a midfielder to clear a spot. Getting rid of the on-loan and underperforming Bakayoko would make sense.
He likely won't see many chances at Stamford Bridge, as Chelsea manager Maurizio Sarrihas a tendency to stick by a small group of players he trusts. Ruben Loftus-Cheek is still waiting for his shot, and he would undoubtedly sit ahead of Bakayoko in the pecking order.
If he does return in January, another loan seems likely. More consistent playing time at a smaller club could help Bakayoko rebuild his transfer value.