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Benayoun, 31, was brought to Stamford Bridge last summer by former manager Carlo Ancelotti but has fallen down the pecking order under current coach Andre Villas-Boas.
Although Liverpool have first option on the midfielder – having sold him to the Blues previously – they reportedly do not want the Israeli back, but Arsenal, Tottenham and Lille have shown an interest in his services.
Meireles, 28, is seen as good competition for midfield positions by Villas-Boas, and the Portuguese coach could put another offer on the table for the player before transfer deadline day passes.
Chelsea’s determination to sign Luka Modric from fellow London club Tottenham has not lessened either, and Benayoun could be used as a makeweight in a deal.
The Blues have also bid £17.7m for left-sided Porto player Alvaro Pereira, who played under Villas-Boas last season.
It falls around £8m short of the Uruguayan star’s contract clause but Chelsea believe his willingness to come to the Premier League side will work in their favour.