Terry was taken off on a stretcher with an injured arm in the first half and Drogba jarred his knee near the end of the match.
"Terry hasn't broken his elbow but we need to wait and see," Grant said. "If it was down to his character he would be sure to play, but it's up to the medical team," Grant added.
Terry returned after an x-ray to lead his team on a lap of honour and said he was optimistic he would play.
On Ivory Coast striker Drogba, Grant said: "It doesn't look so good but we need to wait. We have 10 days."
Grant said his side should be proud of what they had achieved by reaching the Champions League final and running Manchester United so close in the league despite the squad suffering a host of injuries.
"But we must congratulate Manchester United and Alex Ferguson. He's a great manager and a great person and I like him personally," he said.