Plans to expand Anfield further may not go ahead because Liverpool are worried about fans being angered by the ticket price rises needed to fund it.
"Ticket prices are an issue in England," said owner John Henry. "That may foreclose further expansion."
A fans' group called the news "disappointing", adding it would like clarification on the situation.
Liverpool's redeveloped main stand has increased Anfield's capacity to 54,074.
That is an increase of about 8,500 seats and plans for the next phase of the redevelopment would see the Anfield Road end extended, adding another 5,000 seats.
But Henry said: "I don't know if there will be a next step."
Last season, Henry's Fenway Sports Group apologised to fans and reversed plans to increase ticket prices after supporters staged a walkout during the 2-2 draw at home to Sunderland.
"These comments are a little surprising and disappointing for some supporters." said James McKenna from the Spirit of Shankly fans' group, who were involved in February's protest.
"There is outline planning for the work and it seems a little disingenuous that we have never been told that ticket prices would impact the decision to redevelop the Anfield Road end.
"At a time when the club has increased revenues, to suggest that making an extra million pounds or so would prevent further expansion going ahead is a little strange; maybe John Henry should clarify what he means."
'More discussion needed over Champions League'
Meanwhile, Henry says Premier League owners are "not happy" at Uefa's plans to alter the way Champions League prize money is distributed.
Uefa wants to give more money to clubs who have historically performed well in the competition.
That would benefit five-time winners Liverpool and other European giants such as Real Madrid, who hold the record with 11 titles.
However, it would lead to a decrease in cash for sides like Manchester City, who have never won the competition.
The changes were only agreed by a small number of club officials and Uefa prior to them being unveiled in August.
"They unilaterally made changes to the market pool and there should have been I think more discussion," said Henry, whose club did not qualify for European competition this season.
"But I can tell you that the [Premier League] owners were not happy... at least among the clubs that I speak with."
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