Costa has come to symbolise the club's transformation under Antonio Conte.
Costa has come to symbolise the club's transformation under Antonio Conte and ensured the Blues extended their winning streak to nine Premier League games with the winning goal against West Bromwich Albion on Sunday.
That goal, Costa's 12th in 15 league appearances this season, moved Conte's side back three points clear at the head of the table ahead of the midweek trip to face bottom club Sunderland at the Stadium of Light.
And the manner in which the Brazil-born Spain striker created and scored an excellent individual goal in the final moments of the game recalled memories of the inspirational Drogba.
The former Ivory Coast international spent nine years at Stamford Bridge, delivering a succession of trophies to the club -- including famously scoring the decisive penalty that secured them the Champions League.
Cahill believes there is a comparison to be made between Costa - who is now in his third season at the club - and the Ivorian.
"Didier was a huge figure goal-scoring wise and also with his personality on and off the pitch," said Cahill.
"You need strikers like that and Diego has fitted in nicely. Since he's been at the club he's scored goals but this season he's on fire.
"Are the fans starting to love him like they loved Didier? Yes of course because he is banging goals in every week. He is winning us matches.
"At this moment he is right up there among the best in the world. The statistics don't lie."
Costa's talents have been apparent since he arrived at the club while the forward has also developed a reputation for a fiery temperament.
But he has been noticeably more restrained during the club's recent revival, going ten matches without a caution.
"He is not getting as frustrated as he used to. He is channelling (his energy) in the right direction now and is being patient," said Cahill.
"I haven't had to have a word with him about it, I think that's something he has added to his game this season."
Conte has no fresh injuries to contend with but may opt to start with Willian ahead of Pedro.
Sunderland manager David Moyes has conceded his side need to embark on another run of good form after the 3-0 defeat at Swansea saw them return to the foot of the Premier League table.
The Black Cats had won three of their four previous games, but with the bottom six clubs separated by only four points, a similar sequence of victories will boost their bid to pull off a fifth consecutive successful relegation battle.
Certainly they are in a better place formwise than when they failed to win any of their first 10 games.
"As a club, we've been in this situation many times before so it's not something that's new to us," said Moyes.
"Those recent three wins in four put us back in with a fighting chance, when a few weeks ago we weren't in with one. We probably need to go on a similar run like that another two or three times this season."