Chelsea had an opening offer of £60m rejected last month but returned with an improved figure as head coach Mauricio Pochettino seeks to bolster his midfield options following the departures of Mateo Kovacic to Manchester City and N'Golo Kante to Al Ittihad.
Although their latest proposal has been turned down, Chelsea are expected to continue their pursuit of Calcedo, who is valued by Brighton at £100m.
Caicedo, 21, has joined up with Brighton in the United States for their preseason tour, and the club are in a strong negotiating position given he signed a new contract in March that runs to the end of the 2026-27 season.
Brighton rejected offers from Arsenal and Chelsea for Caicedo in January. Mikel Arteta's side subsequently turned their attentions to Declan Rice and competed a deal worth up to £105m with West Ham for the England international.
That transfer is viewed as something of a benchmark by Brighton, who believe Caicedo is at a similar level.
Chelsea, meanwhile, have said that defender Wesley Fofana has undergone ACL reconstruction surgery after he was hurt shortly before the team were due to fly out to the U.S. for their preseason tour.
"The 22-year-old did not travel to America for the club's pre-season tour due to specialist medical assessments, which unfortunately confirmed that an operation would be required," the club said in a statement.
"Wesley will now begin his recovery and work with the club's medical department at Cobham during his rehabilitation phase."