John Fenty, majority shareholder at the League Two outfit, has told BBC Sport that he would welcome a job application from the former England defender.
"I'm surprised we haven't heard from Sol. He said that clubs aren't taking a punt on young managers. We'd have a chat with him," he said.
"There is a lack of players and ex-pros wanting to be managers. We've had no applications from people who have just left the game and that's rather surprising.
"We'd like to get it out there that we are looking for younger managers to apply.
"We gave an opportunity to Brian Laws and he went on to manage nearly 1,000 games. We gave Paul Hurst a chance and he is now one of the most highly rated managers in the Football League, doing a great job at Shrewsbury."
Campbell was recently linked with the managerial vacancy at Oxford United, a role for which former Liverpool forward Craig Bellamy is believed to be the favourite.