Rochdale came in to end Coleman's 13-season association with Stanley last month and his lengthy stint at the Crown Ground means searching for a new manager is a novel experience for Heys and his boardroom colleagues.
"The big thing is this is the first time that any of us at the club have had to appoint a manager," he told Accrington's official website. "We'll certainly be seeking advice from other people and it's something that we've got to get right.
"John Coleman was here for 13 years and we want the next person who comes in to be here for that length of time as well. We're not a club that looks to sack managers as soon as something goes wrong.
"We want to make sure we've got the right person in terms of working with the board, working with the people at the club and the players.
"It will be someone who fits in well, knows what we expect and who has a long-lasting relationship with Accrington Stanley."
