Shareholders and members of the Pompey Supporters Trust (PST) are in favour of retaining representation on the club’s board in the event of a takeover.
Eisner is in exclusive negotiations with Portsmouth until 1 June.
The PST, which currently owns 48% of the club’s shares, has three members out of nine on the board.
In a statement, the PST said: “Given we represent the largest share in the club, we would hope to see our members’ views on supporter ownership and involvement, and protection of the club’s heritage, reflected in any bid.
“Ultimately, it will be our shareholders and members who will vote to decide whether this, or any other bid for the club, is successful.”
More than 2,000 people responded to the survey on hopes, concerns and opinions relating to an ownership change over a week-long period.
It revealed 64% initially felt positive about Eisner’s interest, rising to 74% the more they heard about his intentions.