"The club will continue to look to improve the squad and remain hopeful of closing in on several new signings ahead of the Barclays Premier League campaign."
Carson joined Liverpool from Leeds for £750,000 in 2005, but spent last season on loan at Aston Villa, making 35 Premier League appearances.
The proposed £4m fee marked a major reduction in the player's asking price, with Liverpool previously holding out for around £10m.
Aston Villa had been favourites to sign Carson on a permanent basis but manager Martin O'Neill's interest appeared to cool with Tottenham keeper Paul Robinson emerging as a more likely target for the Villans.
Liverpool, who have already sold Peter Crouch to Portsmouth this summer, are keen to free up transfer funds as they look to finalise a deal for Villa captain Gareth Barry and continue to chase Spurs striker Robbie Keane.
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