Liverpool want a decision from off contract Chelsea winger Joe Cole this week.
The Sun says the England star has been offered £90,000 per week for three years - over £13million in total.
But Cole, 28, has yet to agree and Liverpool fear Tottenham or Arsenal could improve their bids.
Liverpool are in advanced talks with Cole's agent and want the former Chelsea midfielder to seal the move quickly.
But Cole, available on a free transfer, is keen to play in the Champions League.
Instead Liverpool hope to lure him with the promise of first-team football and a run in the Europa League.