The 26-year-old’s contract is set to expire at the end of the season and the forward will be available on a free transfer.
Liverpool have long been linked with a move for the highly-rated forward, but Benitez have now conceded defeat in his bid to sign the Morocco international.
“I think that we will not sign him – but I will not say [any more],” said the Liverpool boss.
Chamakh revealed on Monday that he would be keen on a move to Arsenal in the summer.