Wrexham were relegated from the Football League in 2008
Wrexham director Spencer Harris says they would seek new investment if members of the Supporters Trust voted in favour.
The club has been owned by Wrexham Supporters' Trust (WST) since 2011.
Fans have started an online petition calling for the board to actively seek investment and say fan ownership has not worked.
"It's up for the members who instruct the board in what they wish us to do," he said.
"The board of directors are there to serve the wishes of the owners of the club. If membership wants us to sell the club then that's what we would do.
"But I've never attended, as of yet, a single meeting where that's been an agenda item from our owners.
"It's not come up in an AGM or resolution which members are freely able to do.
"If the membership and the owners, who are the fans, wish the club to do then that's what we'd do."
Spencer Harris has been on Wrexham's board of directors since November 2011
The National League club's board issued an apology to fans after they slipped to the bottom of the National League - their worst-ever league position.
Wrexham are in their 11th season in the fifth-tier of the English football pyramid and in danger of dropping into National League North.
"I'm sure some of our fans will be worried and concerned about that as are we all," Harris said.
"But that's not in our thoughts, our thoughts are swiftly climbing the table.
"It's a really difficult position after finishing in a decent position in fourth last season
"It just hasn't worked on the pitch this season and for whatever reason the chemistry hasn't been right on the pitch, we've been missing key players and things have gone against us.
"To find ourselves in a very difficult position with 20 odd games of the season gone is not great.
"Confidence has been hit in the team and it's up to the manager to help turn that around."
Harris confirmed funds for loan signings as well and recruitment during the January transfer window would be available to manager Dean Keates.
