Terry collided with goalkeeper Petr Cech and Bolton striker Kevin Davies and was stretchered off during the 1-1 draw at Stamford Bridge.
Terry went to hospital for X-rays but returned to lead the Blues players out at the end of the game for their
lap of honour with his arm in a sling.
It was revealed the arm was not broken, but he has a partially dislocated elbow, and Terry said he would be fit to train after "three or four days" and be fit to take on Manchester United in Moscow.
Grant, however, was more cautious, saying: "We will know if he is fit for the final in a few days.
"He is strong enough to recover but we will wait and see.
"In 10 days we play the final so we will take a decision nearer the time. We need to see that he is fit to play."
Grant says he was concerned about the fitness of Drogba.
The striker got a kick on his left knee 10 minutes from time against Bolton and the Chelsea boss admitted he was struggling.
"He could not come off because we had used all our substitutes," said Grant.
"He did everything to finish the game.
"It does not look so good but we need wait again."
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