According to Forbes, the current deal between the two parties ends in mid-2010, and the brewer held an exclusivity agreement which prevented the club from exploring other options until July this year.
"We will have a conclusion of a deal or not this year. But, like in every discussion, everything has a price, and we need to assess the alternatives," Carlsberg chief executive Jorgen Buhl Rasmussen told the magazine.
Stefan Szymanski, sports economist at the Cass Business School at City University in London, added: "If I were a brand, I wouldn't want to be associated with a football team for so long, as you end up alienating supporters of rival teams. And advertisers don't want their products to be permanently associated with just one team."
Shares in Carlsberg rose 5.3 per cent in afternoon trading after the company beat forecasts for its second-quarter results. The firm also said it had gained market share in Eastern Europe and Asia.
Carlsberg has been the Anfield side's official sponsor since 1992, the longest partnership in the English Premier League.
