Liverpool have two outstanding cases against Fenerbahce over outstanding fees for Lazar Markovic and a friendly that took place on 14 July 2016.
The Markovic case is being processed by the FIFA Players Status Committee and the Reds stand to be paid €367,808 pending the outcome.
Liverpool will be awarded €1m in addition to interest and extra costs if they win their CAS case for the friendly game.
Fenerbahce disclosed the details of all ongoing cases the club is involved in a statement on the Public Disclosure Platform.
Markovic spent the 2015-16 season on loan at Fenerbahce in a campaign disrupted by injuries.
The Serbia international scored twice and provided three assists for the Yellow Canaries.
The cases against the Super Lig outfit are outstanding from the previous board under the leadership of former club president Aziz Yildirim.
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The club has a new president after Ali Koc defeated Yildirim in the Fenerbahce elections last month.
Koc has pledged to make sweeping changes starting with getting the club finances in check.
The Super Lig side have appointed Damien Comolli as sporting director, Phillip Cocu as manager and brought in three players thus far this summer, Ferdi Kadioglu from NEC and Berke Ozer as well as Baris Alici from Altinordu.
Fenerbahce finished last season as runners-up and will have to navigate past a tricky playoff round to reach the Champions League group stage.
