The centre-back has been out of action since November 11 when he sustained the problem against Liverpool and is now hoping he can be back in time to make the trip to Japan to take on Ulsan Hyundai or Monterrey n the semi-finals.
The Blues have three fixtures prior to that - this weekend's Premier League trip to West Ham United, Wednesday's vital Champions League clash with Nordsjaelland and next weekend's league meeting with Sunderland - but manager Rafael Benitez suggests Terry won't make at least the first two of those.
"Yeah, it could be (that Terry travels without playing a match prior)," said the Spaniard.
"It's a question of confidence. When you forget you have that problem in your knee is when you are ready."
He added: "He's pushing - 'I want to be there, I want to be involved' - but still he will need some time.
"It's a knee, not just a muscle. You have to see the reaction when you turn.
"You cannot put him in a position where he could get injured again."