The cost of redeveloping the Anfield Road end of Liverpool's stadium "is not a smart investment", says chief executive Ian Ayre.
Liverpool opened the redeveloped Main Stand last month, raising capacity to 54,074, and have planning permission to extend Anfield Road by a further 4,800.
But Ayre said: "A stand behind a goal doesn't have the benefit of hospitality that would go a long way to meet the redevelopment costs."
The upgrade would cost about £60-70m.
Club owner John Henry has previously played down the prospect of the work going ahead on the basis ticket prices would have to rise to cover the cost.