Drogba watched the 3-1 victory over Sunderland in December with Hiddink and Blues owner Roman Abramovich following the sacking of Jose Mourinho.
Hiddink later confirmed he would like to add the Ivorian to his backroom staff at Stamford Bridge and Drogba’s current club, Montreal Impact, have revealed they are in talks with the Blues.
“I had a very good relationship with [Drogba] last year,” Courtois told reporters. “He was great for the dressing room and our team.
“If he comes back as a coach it will be a great addition to all the team.”
Chelsea are unbeaten since Mourinho’s departure, winning two out of their four matches and most recently recording a convincing 3-0 win at Crystal Palace.
Courtois insists the club’s players must take as much responsibility for their poor start to the season as Mourinho but admitted the change had drawn a positive reaction.
“It's something psychological and sometimes it changes with little changes,” he explained. “Maybe we needed a little change to pick up our level.
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“In football it's always like that. When results are not good the first thing they look at is the manager. But I don't think it is only the manager, the players have to take responsibility as well.
“We were the ones who were not playing as well. With a new manager some things changed. Maybe with some players the mentality changed.
“We of course know we were responsible as well. We had team meetings where we said, ‘OK, the manager has gone, but we are responsible as well and we need to pick up our levels because we are not good enough for being a Chelsea player.’ Now we are stepping up our game.”
On the differences between Mourinho and Hiddink, Courtois added: “Obviously training is a little bit different - the approach [Hiddink] has sometimes in how he wants to train.
“Maybe sometimes a bit more tactical, a bit less, different types of little games we play or shooting the ball to give confidence to the strikers.
“Sometimes he is more outside of the training, more observing and leaving the training more to [assistant first-team coaches] Steve Holland and Eddie Newton.
“He just steps in when he thinks he needs to explain something to the team. When he explains he explains it well. Every manager has his way of working.”