Liverpool will follow up the signing of Charlie Adam with an improved offer for Stewart Downing - but they still face a fight to persuade Aston Villa manager Alex McLeish to sell the England winger.
Villa turned down Liverpool's opening £15million bid and BBC Sport understands they are refusing even to consider a price for Downing, despite speculation that they will sell for £20million.
Downing is expected to hold further talks about his future with McLeish on Friday and Liverpool's improved offer, likely to be around £18million, could even have arrived by then.
Liverpool boss Kenny Dalglish is keen to make the 26-year-old his third signing of the summer after concluding a deal for Sunderland's Jordan Henderson and completed the signing for Blackpool's Adam, and the player is eager to make the move to Anfield, particularly since talks on an extended contract at Villa Park stalled.
Read more: BBC Sport
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