Sky Sports said Palace captain Guehi, who scored in his side's 3-0 win at Aston Villa on Sunday, was having a medical in London ahead of the closure of the transfer window at 17:00 CET.
Liverpool are also expected to announce the completion of the British record 125 million-pound signing of Newcastle United's Sweden striker Alexander Isak.
Should both be confirmed, it would complete a remarkable double for Liverpool and take their summer spending towards the 500 million pounds mark.
Guehi, who came through the ranks at Chelsea and had a loan spell at Swansea City before joining Palace in 2021, has been a fixture in the England squad since his first senior cap in 2022.
He was part of the Palace team that won the club's first silverware last season, beating Manchester City in the FA Cup final, and is a favourite with the Palace fans.
The news that he is set to leave for Anfield will be a big blow to manager Oliver Glasner, who on Sunday said that the club 'had to keep him'.