Swansea City Supporters' Trust is considering taking legal action over the sale of the club's shares, a meeting was told on Thursday.
Americans Jason Levien and Steve Kaplan secured 68% of shares in July this year, with the trust retaining 21.1%.
The supporters claim they were not consulted and were not able to buy more shares themselves.
A statement on the Trust's website said it had received legal advice, but no decision had been taken.
"We are conscious any legal action would create uncertainty," the statement said.
"Our first preference has always revolved around protecting our shareholding and influence at the football club.