The appointment of Brendan Rodgers last week means Clarke, number two to predecessor Kenny Dalglish, will leave Anfield.
Rodgers has yet to name a number two but Liverpool and the 39-year-old’s former club Swansea have agreed a compensation package which sees three of his backroom staff move to Anfield, including his Liberty Stadium assistant Colin Pascoe.
Performance analyst Chris Davies and head of sports science and medicine Glen Driscoll have also joined the Reds.
Clarke, 38, offered his resignation last month following the departure of Dalglish but it was declined by the club.
The former Scottish international has previously held similar roles at Newcastle, West Ham and Chelsea — for whom he played more than 300 games between 1987 and 1998.
Meanwhile, Birmingham manager Chris Hughton has been granted permission to speak to Norwich.
The Canaries are in the market for a new boss after Paul Lambert completed a switch to Aston Villa recently.
Hughton has been heavily linked to the managerial vacancy at Blues’ neighbours West Brom, but the 53-year-old former Republic of Ireland full-back is now set for talks at Carrow Road.
Elsewhere, Branislav Ivanovic is unsure whether he will be at Chelsea next season after distancing himself from claims made by a man claiming to be his agent in the Italian media.
Vlado Boroza told Radio CRC that Blues right-back Ivanovic had no intention of quitting Stamford Bridge despite speculation linking him with Napoli.
Ivanovic yesterday denied any association with Borozan, however.
“I’ve seen in the press that an agent called Vlada Boroza has been saying things on my behalf. I would just like to put on record that he is not my agent and does not have the right to tell the press anything on my behalf,” Ivanovic told Sky Sports.
The Serb’s performances have reportedly caught the eye of Spanish League Champions Real Madrid, and the player is unsure of his future despite being contracted to Chelsea until 2016.
“With regards to speculation about my future, we will see what happens,” he added.