The Ecuador international has supposedly been the subject of one failed bid from the Blues, whose opening £70m offer was quickly rejected by the Seagulls.
Brighton are under no pressure to sell Caicedo, whose contract at the Amex Stadium runs for another four seasons, but they will likely relent if a suitable offer comes in.
Caicedo memorably stated his desire to leave Brighton in January when Arsenal had two bids rejected, but the Gunners opted to move for West Ham United's Declan Rice this time around.
Arsenal's withdrawal from the race pushed Chelsea to the head of the queue, and according to the Daily Mail, the West London giants are now ready to make a revised offer.
The report claims that Brighton will be offered £80m plus add-ons for the 21-year-old, who has been promised that he can leave for a club-record fee in the summer transfer window.
The Seagulls were initially thought to have been willing to accept the £70m that Arsenal were offering in January, but they have had a change of heart after the Gunners shelled out £105m on Rice.
Now, Brighton are also said to be demanding a nine-figure sum to part ways with Caicedo, whose agents are understood to be pushing for his proposed switch to Stamford Bridge to go through.
Caicedo is supposedly close to agreeing personal terms with Chelsea, who will face their South Coast counterparts in Philadelphia on Saturday as part of the friendly Premier League Summer Series.
The midfielder attracted glances from Manchester United during his time with Independiente del Valle, but the Red Devils ultimately decided against a deal, allowing Brighton to pick him up for just £4.4m.
Caicedo has since scored two goals and set up three more in 53 appearances for Roberto De Zerbi's side, playing a crucial role in their successful push for Europa League qualification last season.
Chelsea are noticeably thin on the ground in midfield at the moment, having allowed Mateo Kovacic, Mason Mount, Ruben Loftus-Cheek, N'Golo Kante and Tiemoue Bakayoko to depart this summer.
Conor Gallagher could also be offloaded amid links with Tottenham Hotspur and West Ham United, but the Blues are not believed to have received any bids for the Englishman yet.
Enzo Fernandez, Carney Chukwuemeka, Cesare Casadei and Andrey Santos make up the rest of Chelsea's midfield options, and the latter three all started Wednesday's 5-0 thumping of Wrexham in North Carolina.