Liverpool chief executive officer Ian Ayre has said it would cost over £60 million to redevelop the Anfield Road end of the ground.
Planning permission is reportedly in place to extend the Anfield Road end and put in an extra 6,000 general admission seats, but Ayre believes the club need to find a "rounded solution" due to the time it would take to repay the cost of the redevelopment.
Liverpool opened the new Main Stand in September, which has taken Anfield's overall capacity to over 54,000.
The club's principal owner, John Henry, recently suggested that supporters' protests over ticket prices had put further plans to expand Anfield in doubt.
"A stand behind a goal doesn't have the benefit of hospitality that would go a long way to meet the redevelopment costs," Ayre said in minutes of the most recent Liverpool supporters' committee meeting.
"If you consider the redevelopment of Anfield Road from a purely general admission perspective, building, say, 6,000 extra seats to take the capacity up to 60,000 would cost somewhere between £60m and £70m.
"At £12,000 to £13,000 per seat, it would take approximately 15 years to pay back, which is not a smart investment for the business. Therefore the club needs to find a rounded solution that's in the best interests of the football club."
Ayre, who is leaving Liverpool at the end of this season, added: "The club's objective was always to build and open the Main Stand. From the outset, the club did not want to set deadlines or promises it failed to keep.
"The club now needs a period of time to ensure that what it has put in place works, and in tandem continue with plans for Anfield Road.
"However, as with the Main Stand, the club has to find the right economic model, and only then will it be the right time to move forward."