Brighton sold Belgian winger Leandro Trossard (28) to Arsenal this month for 27 million pounds. British media reported they were not interested in selling Caicedo too after he impressed in central midfield this season.
The Ecuador international said he was grateful to Brighton and its owner Tony Bloom for giving him the chance to play in the Premier League but did not want to miss out on a "magnificent opportunity".
"I am the youngest of 10 siblings from a poor upbringing in Santa Domingo in Ecuador. My dream (was) always to be the most decorated player in the history of Ecuador," Caicedo wrote on Instagram.
"I am proud to be able to bring in a record transfer fee for Brighton which would allow them to reinvest it and help the club continue to be successful.
"The fans have taken me into their hearts and they will always be in my heart, so I hope they can understand why I want to take up this magnificent opportunity."
A fee of 60 million pounds would be a record for Brighton, who sold Marc Cucurella (24) to Chelsea in August for an initial fee of 55 million pounds, potentially rising to 62 million pounds in add-ons.
Brighton are sixth in the standings halfway through the season and are in a strong position to qualify for European football for the first time in the club's history.
On Friday, Brighton boss Roberto de Zerbi had said he hoped to convince Caicedo to stay.
"I spoke with him like a father, not like a coach," he told reporters. "I hope he can stay with us until the end of the season... That's the best solution for him and for us."
Arsenal are chasing their first league title since 2003/04, looking for cover in midfield after Mohamed Elneny (30) suffered a knee injury, with no timeline on the Egyptian's return.
The transfer window shuts on Tuesday.
