The Russian clubs claim they have agreed personal terms with Benayoun's agent and that a £7.5million offer is on the table for the Israel midfielder.
Target: Liverpool's Yossi Benayoun
Russia's transfer window is open until the end of the month but with England's closed Benitez knows he would not be able to buy a replacement.
Meanwhile, Valencia and AC Milan remain serious rivals to Liverpool for Milan Jovanovic.
Liverpool were confident they had a deal agreed in principle with the Standard Liege striker but his agent Cvijan Milosevic said: 'He has not made up his mind. He went to see Milan after their match against Palermo and there is also a concrete interest from Valencia.'
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