The 21-year-old has been strongly linked with a move away from the Amex Stadium since developing into a key player for the Seagulls over the past 12 months.
Caicedo was signed for Brighton by former head coach Graham Potter - now at Chelsea - in February 2021, joining from Ecuadorian side Independiente del Valle for £4.5m.
After a brief spell on loan with Belgium outfit Beerschot during the first half of the 2020-21 season, Caicedo returned to Brighton in January last year and has since featured regularly in the first team, scoring twice in 29 appearances across all competitions.
The deep-lying midfielder is said to have attracted interest from a number of top European clubs, including Premier League duo Liverpool and Chelsea and La Liga giants Real Madrid.
A recent report claims that Chelsea have identified Caicedo as a potential target if they fail in their pursuit of Benfica's Enzo Fernandez.
However, a separate report states that the Seagulls midfielder has told friends that he would like to secure a move to Liverpool and work under Jurgen Klopp.
The Reds are in the market for a new centre-midfielder, with James Milner, Alex Oxlade-Chamberlain and Naby Keita all out of contract at the end of the season.
Caicedo is under contract at the Amex until the summer of 2025 and Brighton were thought to have placed a price tag of around £85m on the youngster.
However, The Mirror reports that both Liverpool and Chelsea have been handed a boost in their quest to land Caicedo, as Brighton could now entertain offers in the region of £60m plus add-ons for the midfielder.
Earlier this month, Brighton CEO Paul Barber revealed that the club are yet to receive any offers for the midfielder and also responded to joking comments made by Potter last season that a £42m bid would not even be enough to get Caicedo's boots.
Speaking to CBS Sports, Barber said: "I'm pleased to say we haven't had any (bids for Caicedo). Maybe Liverpool haven't got my email because I haven't seen any.
"I'm not sure £42m will even include the boots now, maybe just the laces. But joking aside, every player's value is ultimately determined by the market. Graham's comments were part in jest but part serious because Moises has been an exceptional player for us.
"Since he came to the Premier League, he has developed all the time. He's a young man with a great attitude, fantastic work ethic and a very nice human being off the pitch.
"So all those things contribute to the value of a footballer should it come to that moment to sell."
Caicedo is expected to play against Liverpool when Brighton welcome the Reds to the Amex in the Premier League on Saturday.