The 23-year-old attacking midfielder limped off during the pre-match warm-up ahead of Chelsea's 5-1 win against West Ham and sat out their 2-0 victory over Fulham before the international break, and manager Enzo Maresca has confirmed Cole is still recovering.
Asked for an update, he said: "Cole took part in the session yesterday for the first time.
"Not the entire session. We have one more session, we are going to try with him. We will see if it is okay.
"Otherwise, he will be out again tomorrow. He is recovering from an injury. It is not managing him, it is recovery."
The Blues will be without Liam Delap for up to 12 weeks after he suffered a hamstring injury against Fulham and, to add to their woes, new signing Alejandro Garnacho is not fully fit.
Enzo said: "Liam is around 10 to 12 weeks. Long way to go!
"He [Garnacho] is working well. For sure, he needs to work. He arrived not 100 per cent fit.
"He needs to work and is working well. We will see. Hopefully, soon we can give him minutes."
Meanwhile, the manager wished Nicolas Jackson luck after he joined Bayern Munich on loan.
He said: "Nico is quite easy. In this moment, he is a Bayern player, I sent him a message and wished him all the best.
"He was very good and was working well. I wish him all the best."