Liverpool are believed to have tabled a £3.5m bid for Real Madrid striker Fernando Morientes.
Boss Rafael Benitez wants Morientes to strengthen his team, with Djibril Cisse out for the season with a broken leg.
BBC Sport understands that Liverpool have been told to double their bid for the 28-year-old Spanish international.
Morientes, who has lost his place at the Bernabeu following the arrival of former Liverpool striker Michael Owen, is also wanted by Monaco.
Liverpool believe Morientes is keen to move to Merseyside and hope a compromise deal of £5m can be agreed.
Morientes said: "To play for Liverpool would please any player and in Rafa Benitez they have a technical coach who I have always appreciated.
Is that a joke offer? Great if we can get him for that but I think £8m might be required
From Matthew
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"But there are a lot of things to sort out. I haven't spoken directly with Benitez but I know Liverpool want me."
Morientes was the top scorer in last season's Champions League while he was on loan at Monaco.
However, on his return to the Bernabeu he has found himself behind Raul, Ronaldo and Owen in the pecking order.
Morientes was thought to favour a permanent move to Monaco but he admits that now looks unlikely.
"I had a good time in Monaco last season but I have not heard anything from them lately," he said.
"My situation is difficult but Madrid know they must do something about me."