It is understood that there is disagreement among Carlsberg chiefs as to whether to continue with the sponsorship, which expires in May.
The exit of star player Michael Owen, a key draw for any brand looking to sign a sponsorship deal, allied to speculation surrounding captain Steven Gerrard's future at the club, as well as its ownership, have led to questions being raised internally over the value of the shirt deal.
However, a Liverpool FC spokesman insisted negotiations with Carlsberg were ongoing.
In August Carlsberg increased its reach across the Premier League by ousting rival Carling to become the official beer of London club Tottenham Hotspur. It marked the brewer's seventh such deal with a Premiership club.