Liverpool were last night preparing to raise their bid for Yossi Benayoun to £4.5m - with West Ham United keen to do a deal if they can persuade Craig Bellamy to move to Upton Park.

The revised offer from Liverpool, who had initially offered £3m, comes close to the £5m that West Ham hoped to receive for the Israel international. The likelihood is that Liverpool will eventually agree to pay especially as Benayoun is desperate to join them.

West Ham have grown frustrated with the 27-year-old midfielder after he reneged on a verbal agreement to sign a lucrative new contract. That offer has subsequently been withdrawn but it will be tabled again if Benayoun, who has two years left on his current deal, pledges his future to West Ham when he returns from holiday next week.

Benayoun has been trailed by the Liverpool manager Rafael Benitez for some time. The Spaniard came close to making a bid last summer, as did Arsenal, and The Independent revealed earlier this month that Benitez was now determined to sign Benayoun, who first came to prominence at Racing Santander before joining West Ham two years ago for £2.5m.

Benayoun had threatened to hand in a transfer request when he held talks with West Ham at the end of the season. However, it had appeared that a new deal - doubling his pay to around £50,000 a week - and reassurances that he will play more regularly had persuaded him to stay. But once he became aware of Benitez's renewed interest Benayoun informed West Ham that he wanted more time before signing.

West Ham were determined to keep the player but after losing out on Darren Bent, with the Charlton striker changing his mind at the 11th hour on a £18m move, they have turned their attentions to Bellamy. The Welsh international can leave Anfield although his £12m valuation - twice what Liverpool paid Blackburn last summer - has scared off potential bidders.

West Ham will hope that if they offer a reduced fee plus Benayoun for Bellamy, then it will help secure the deal especially as they will also increase his wages. They regard Bellamy as an ideal partner for Dean Ashton, which further indicates that Carlos Tevez is leaving.