Square1, formerly Holborn PR, is working with a third party involved in the possible Dubai International Capital (DIC) deal and has been talking to journalists about the bid.
Liverpool is currently under controversial American ownership, which has prompted protests from fans. DIC looked set to buy Liverpool 18 months ago and is rumoured to still be interested.
Brunswick was used during the initial bid and is DIC's retained agency (PRWeek, 8 December 2006).
The takeover by US duo Tom Hick and George Gillett was seen in many quarters as a huge PR success.
But since then, relationships between the owners, manager Rafael Benitez and Liverpool supporters have soured considerably.