Caicedo was the subject of a rejected £60m bid from Arsenal on Friday after Chelsea also had their own offer turned down by the Seagulls last week.
Brighton boss Roberto De Zerbi has asked Caicedo to stay until the end of the season but the Ecuadorian has released an open letter asking to leave the AMEX stadium.
"I am grateful to Mr Bloom and Brighton for giving me the chance to come to the Premier League and I feel I have always done my best for them. I always play football with a smile and with heart," Caicedo's statement read.
"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.
"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."
The 21-year-old has only made 26 Premier League appearances since joining Brighton from Independiente del Valle in 2021.
Caicedo starred for Ecuador at the 2022 World Cup in Qatar, scoring once in the tournament.
