Anzhi Makhachkala are reported to be keen on the Senegal international after Cisse was on the score-sheet when they met Newcastle in the Europa League this season.
Russian newspaper Izvestia has reported the cash-rich club from Dagestan are ready to offer the equivalent of £15.4million to secure his services.
In addition, they are said to be ready to pay the player around £50,000 a week in wages and hope the lure of another season of European football, something he will not get on Tyneside this time around, will prove attractive too.
Guus Hiddink's side were linked with Cisse before his move to England, but agent Nickolay Guido says they will face competition for his signature should they make an approach.
Nickolay Guido: "Russian clubs have shown interest in Papiss at the same time, but I don't want to name the names of the clubs as it wouldn't be a correct step from me.
"Anzhi have the advantage that they could qualify for the Europa League and the Senegalese striker's dream has been to show his qualities in Europe and it doesn't seem possible with Newcastle in the near future."
Newcastle owner Mike Ashley is not averse to selling a player if the price is right, as it was with Andy Carroll in January 2011 when Liverpool offered a staggering £35m for the England international.
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