The 21-year-old Ecuador international had been a target for Chelsea during the current transfer window but Premier League rivals Brighton were determined he would not leave for less than £100 million.
Liverpool have been rebuilding their midfield following the departures of Jordan Henderson and Fabinho.
Caicedo could be reunited with Alexis Mac Allister, the Argentinian World Cup winner who left Brighton for Merseyside in June.
The reported fee would surpass the previous British record of £107 million that Chelsea paid for Enzo Fernandez in January.
It would also represent another huge profit for Brighton, who signed Caicedo from Ecuadorian side Independiente del Valle for just £4 million in 2021.