The 32-year-old is desperate to leave Chelsea in order to get regular first-team football.
Benayoun has one year left on his current contract with Chelsea, but is determined to leave the club before the transfer window closes.
Chelsea are expected to allow the midfielder to return to Liverpool on loan.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.