A senior official, however, insists a final decision on whether to move or redevelop the club's ground has yet to be taken.
According to Billy Hogan, managing director of Fenway Sports Management - the global commercial arm of club owners Fenway Sports Group - the primary consideration has to be ensuring the club can compete financially with their main rivals.
"We see Liverpool as a truly global proposition from a marketing standpoint and a naming rights partnership with Liverpool Football Club is really unlike any other thing there is out there," Hogan told Bloomberg.
"It's something we've seen some interest in and we'll continue to have those conversations."
Hogan added that the final decision will "rest on which opportunity allows us to keep generating revenue to compete with the rest of our competition in the Premier League".
It is believed FSG's preferred option is to increase both the capacity and corporate opportunities at Anfield, as they did when they took over at baseball side Boston Red Sox.
But that could still pose some issues in restricting match-day income and plans for a new build in Stanley Park have not been ruled out.
Under the terms of the agreement struck when plans were first drawn up for the new stadium project the club did have until the end of this month to take up the option of the 999-year lease they agreed with the city council for land in Stanley Park.
With discussions between the two parties continuing, however, that may be subject to change.