Rubin Kazan have reached an agreement to sign midfielder Alex Song from Barcelona.
Brazilian midfielder Fernando completed his transfer from Sampdoria to join Russian club Spartak Moscow on Monday.
Leicester City have completed the signing of Nigeria forward Ahmed Musa from CSKA Moscow for a club record deal worth around £15 million.
Video footage of appeared to show Kokorin and Mamaev in a Monaco nightclub, with waiters carrying dozens of bottles of champagne.
Two Russia players have been fined by their clubs over an ostentatious party following the national team's group stage exit from Euro 2016.
Russia's most capped player, Sergei Ignashevich, has signed a one-year contract extension with CSKA Moscow.