AFC Telford will step up their search to replace for current chairman Lee Carter by advertising for the role.
Carter, who has been Bucks chairman for nine years, is giving up the position to become managing director as the club continue their restructuring.
"We don't want a Mr or Mrs Moneybags to own the club," Michael Frater, vice-chairman of the trust board, says in the advertisement.
"The fans own our club and we want to keep it that way," he added.
"We need a person with true leadership skills and a track record of possibly running a large business or organisation who can deal with the complex challenges ahead.
"Our long-term aim is to get in the Football League.
"It may be a long way down the track but we aim to get there and we want the right person as chairman to help us get there."
Since becoming chairman when the Bucks reformed in May 2004, Carter oversaw three promotions in seven seasons, before Telford suffered relegation from the Blue Square Bet Premier this season.