The state-backed group, who own French club Paris Saint-Germain, were seeking as much as a controlling stake in Leeds United in a deal that would mark Qatar's entry into English football, the FT reported.
"Qatar Sports Investments will be entering English Football, and Leeds is the club of their choice," the report quoted a source as saying, adding that Qatar has been looking at entering English football for the last two years.
Leeds United are holding talks with at least six investors, including the Qatar group, according to the report.
Qatar Sports Investments and Leeds United did not return calls for comment on the FT report.