Fenerbahce said they asked for an extension to complete the deal and held talks with Fifa as “all steps were taken to resolve the issue”.
“Despite this, the opposing club has not completed the transactions without providing any justification to us,” added Fenerbahce.
“As a result of these developments, the transfer process unfortunately could not be finalised.”
BBC Sport has asked Al-Ittihad for a response.
France striker Karim Benzema left Al-Ittihad to join to rival Saudi Pro League side Al-Hilal, external on Tuesday and it appeared En-Nesyri could have been his replacement.
Kante, 34, joined Al-Ittihad from Chelsea in 2023 having won the Champions League, Premier League, Europa League and FA Cup with the Blues.
He also helped Leicester City win the Premier League in the 2015-16 season.