Even the legend himself was called back for a season in 2014, two years after his emotional exit in 2012.
The likes of Samuel Eto'o, Demba Ba, Alvaro Morata, Radamel Falcao and, most recently, Romelu Lukaku have all failed to follow the big man.
In light of Lukaku's loan move to Inter Milan and Timo Werner's recent comments, it looks like the ten-year search will continue this summer.
There was, however, one man who bucked the trend: Diego Costa.
And if there is one thing Chelsea lack right now, it is someone like him.
Tuchel's crisis up front has deepened after Werner said he could 'be happy everywhere' and hinted at disappointment over a lack of game time.
The Blues boss responded: "I'm surprised, I would be very happy as a young guy having a contract at Chelsea Football Club.
"I would be one of the happiest people on the planet. He needs to get his game time by showing quality, take your place and defend your place.
"I would be one of the happiest people on the planet having a contract with Chelsea. If he said this, I do not understand."
After a dismal two years at Stamford Bridge, it feels increasingly likely Werner will be added to that illustrious list of underwhelming Chelsea forwards.
So what was it about Costa that made him so special? Surely, there is a formula the Blues can try to recreate?
Like Drogba, the Spaniard had an intangible edge which made him impossible for defenders to handle.
Besides all the natural qualities of a world-class centre-forward, Drogba and Costa made every single match a fight.
It was an attitude that saw them impact every game, even when seemingly not involved, as centre-backs struggled to get to grips with them.
While Costa was more cynical and nasty, there was an aggression to Drogba's game that no defender could match.
Chelsea need a player who will fight up top, just like Costa.
This is a man who was already fighting legendary Blues physio Billy McCulloch within weeks of arriving at the club.
The feisty forward knew exactly where the line was, somehow picking up only one red card throughout his entire Stamford Bridge career.
That said, Costa would walk that line every time he stepped on the pitch, doing anything to give his team a psychological edge.
He famously took aim at Ryan Shawcross' body odour after squaring-up to the former Stoke captain - and went too far by biting ex-Everton midfielder Gareth Barry.
Chelsea legend John Terry recently revealed this win-at-all-costs mentality extended into training.
He said: "On the training pitch he was incredible, he'd would want to fight you, want to win at all costs.
"That was incredible to have every day."
Costa's provocative style won him the adoration of Chelsea fans and guided the club to two Premier League titles.
Like Drogba, there was a madness and a contentiousness that went alongside the magic.
Every other striker attempting a day in their shoes has just been a bit too… nice.
Alvaro Morata is the best example of a striker with all the necessary talent, but no edge.
As Chelsea hunt for yet another new frontman, they must look to past successes and spot the common denominator.
They need someone who can get mean - and get goals.