Liverpool are set to trigger Christian Benteke's £32.5M release clause in his Aston Villa contract.
The two clubs had been at loggerheads over a deal.
But now Raheem Sterling's £49M move to Manchester City has been confirmed and it is understood Liverpool have relented.
It comes in a week when the Belgian centre-forward had also been linked with Manchester United, who are also on the lookout for a striker.
But the Reds are also hugely interested in bringing in a reliable centre-forward having lost Daniel Sturridge to injury for much of last season and seen the likes of Mario Balotelli flop.
A £32.5M deal would make him the second most expensive signing in Liverpool history.
The 24-year-old could now complete the move over the weekend.
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