Rangers fan shareholder group Club 1872 will vote against the reappointment of chairman Douglas Park at the Scottish Premiership club's annual meeting.
A poll of members drew only 29% support for Park among those who voted.
Club 1872 holds about 5% of the club's shareholding and former chairman Dave King, the largest shareholder, has also been critical of his successor.
But PA Sport predicts that Park, with 12%, is likely to get enough backing on Tuesday to retain his position.
The supporters' group, the club's sixth largest shareholder, will back the reappointment of George Taylor and Julian Wolhardt as directors.
However, it will vote against two resolutions designed to give the board more control over the issuing of shares and equity.
Club 1872 has been critical of the way the club have been run this year and expressed frustration over a lack of communication with the Rangers board.