The Queens Park Rangers striker had been on the verge of a move to Liverpool but could now end up at Stamford Bridge as Jose Mourinho goes in search of back-up options.
The Blues are still awaiting confirmation regarding the severity of Drogba's ankle knock, sustained during the club's 2-1 friendly victory against Ferencvaros on Sunday, and are keeping their options open.
Remy had been set for an 10 million-euro transfer to Liverpool earlier this summer before the move broke down amid reports of a failed medical.
He had attracted interest from Tottenham and Arsenal prior to the Reds making their move, and now Chelsea has entered the frame in the wake of Drogba's setback.
The Ivorian could miss the start of the Premier League season, with the Blues kicking off against Burnley next Monday.
Jose Mourinho had declared his summer spending over in mid-July, with Diego Costa brought in from Atletico Madrid to bolster the club's forward line, but then clinched the signing of Drogba on a one-year deal.
And Mourinho may be forced back into the market to secure another striking option with the severity of Drogba's knock still to be determined.
Remy, 27, has been back in training with QPR and Hoops boss Harry Redknapp hopes he will be fit to face Hull City on Saturday.
"He's here, he wants to work and get in the team," he said. "He's worked really hard on the training ground, I couldn't have asked for any more from him. He's trained great and his attitude's been first class.
"Hopefully with a week's training he'll be fit to play next week."