Gunn has used new signings Michael Nelson and Matt Gill in friendlies so far, as well as stalwart Gary Doherty, but he has made no permanent appointment.
Gunn said: "The captaincy has not been decided as yet.
"Michael Nelson was brought in for his leadership qualities, there's no doubt about that, and he was captain at Hartlepool.
"Matt Gill in the middle of the park is another who showed good leadership qualities, so it's a case of seeing the boys with the armband on and making a decision.
"The more leaders we have on the pitch next season the better."