However, Kadyrov never says outright that he will resign and, according to Radio Free Europe, the outcome has sparked speculation that the Chechen leader wants something from Russian President Vladimir Putin.
Chechnya is an autonomous Russian republic.
Several thousand Chechens, the so-called Kadyrovites, are fighting for Russia in Ukraine.
Russia has in several rounds – 1994–1996 and 1999–2009 – waged brutal wars against Chechen separatists.
Kadyrov came to power in 2007. His rule has been accused of widespread corruption and human rights abuses.