Mauricio Pochettino is desperate to bolster his midfield ahead of the new Premier League season which starts in less than two weeks.
The Blues have sold Mateo Kovacic, Mason Mount and Ruben Loftus-Cheek this summer, while they also released N'Golo Kante after failing to extend his contract.
It leaves Enzo Fernandez, 22, and Conor Gallagher, 23, as Chelsea's two senior figures in the middle of the park.
And according to The Times, Chelsea have drafted up a five-man shortlist, with Ecuador international Caicedo the club's top target.
Chelsea have had three bids rejected by the Seagulls for the 21-year-old, with talkSPORT revealing last week that their latest offer of £80million had been turned down.
Brighton continue to stand firm on their £100m valuation of Caidedo, with it remaining to be seen whether Chelsea match their demands.
And should they walk away from a deal, there are four players who the west Londoners could then pursue.
One of those is said to be Leeds' Adams, who only joined the Whites from RB Leipzig last year, but failed to help keep the Yorkshire outfit in the Premier League.
The Times have claimed that Adams has a relegation release clause in his contract.
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Though with the USA skipper currently recovering from hamstring surgery, it is unclear whether Chelsea will turn their interest into a formal bid.
Southampton's Romeo Lavia is also on Chelsea's radar, who could hijack Liverpool's transfer for the Belgium international.
Alternatively, the 2021 Champions League winners could look to bring Ajax's Edson Alvarez to the English capital once again.
Chelsea failed in their quest to sign the Mexican last summer, who is on the market for around £40m.
And completing Chelsea's shortlist is Celta Vigo's Gabri Veiga following a breakthrough 2022/23 campaign where he scored 11 goals in 36 LaLiga matches.
The Blues are set to announce the signing of a midfielder - Lesley Ugochukwu from Rennes in a £23m deal.
But it is expected that the 19-year-old will be loaned back to France to continue his development.