"Don't believe in fake news. Kante is an Ittihad player now," the club posted in a video message on Twitter.
British media reported the midfielder has signed a contract worth around 86 million pounds a year.
Benzema left Real Madrid after 14 trophy-laden years and signed a two-year contract with the Saudi Arabian champions in a deal reported to be worth more than 100 million euros ($109.17 million).
Kante has been a mainstay at Chelsea, winning the Champions League, Premier League, Europa League and FA Cup during his time with the club.
Kante's last season was plagued by injuries, however, as he missed 38 matches in all competitions with Chelsea struggling without him and finishing 12th in the league.
Several high-profile players have been linked with moves to Saudi Arabia in recent weeks, while Cristiano Ronaldo signed with Al-Nassr in December in a deal reported to be worth around $220 million per year.