Christie-Davies, 20, was not offered a new deal by Chelsea, with his current terms expiring in the summer, and several clubs have been monitoring his situation.
Liverpool took Christie-Davies on trial in March and it appears he has done enough to win a move to Anfield.
He joined Chelsea's academy from Brighton and progressed from the youth ranks to the under-23s, winning the FA Youth Cup in 2015 and 2016 and the UEFA Youth League in 2016.
Christie-Davies is likely to link up with Liverpool's under-23s next season, following former Chelsea teammate Dominic Solanke in leaving Stamford Bridge for Merseyside.