According to reports, Kerkez has agreed to a five-year contract with the English club, and the transfer fee of £40m has been settled.
This move would make Kerkez the fifth most expensive left-back in football.
Before joining Liverpool, Kerkez met with Liverpool's Serbian supporters and took a photo with them, waving the group's flag.
Meanwhile, Bournemouth has already found a replacement for Kerkez in the form of Adrien Truffert, who joined the team last week from Rennes for €17m.