Ivory Coast captain Drogba is committed to playing for his country in the tournament, which starts in January, although he has a knee injury and may require surgery.
Chelsea will decide in the next week whether an operation is required but already know Salomon Kalou, John Obi Mikel and Michael Essien will be away for up to a month when they play in Ghana in the New Year.
When Grant was asked if the tournament should be moved to suit the European soccer calendar in future, he was unequivocal.
“Of course, I think everybody wants it but it doesn't depend on me,” he said.
“We need to think about this. When they started the African Nations Cup there were not so many players playing in Europe. Now the Africans have many players in the Premier League and in other leagues - and in my opinion it will be even more in the next few years.
“So we need to think about this because it’s not good for the players or the clubs. It would be better in the summer but I cannot change it, I can only say my opinion.”
Drogba is 90 percent certain to miss this weekend’s Premier League match at home to Sunderland according to Grant and the timing of his operation could have an impact on his availability for the African Nations Cup.
Grant said Drogba and the club had known about the problem for some months but the striker insisted on playing.