Cooper, 48, quit his second spell as boss at Victoria Park two and a half weeks ago and the club is expected to name their fifth manager in the last four years before next weekend's home game against Coventry, with former Hull boss Phil Brown widely tipped to take over.
"You never know what's going to happen," Cooper said. "When someone new comes into a club the players can react in a really positive way and nobody hopes this is the case at Hartlepool more so than me.
"But whoever comes in is going to find it very hard to keep them up. It's been a difficult last few weeks since I left and results have not picked up. It's been hard for the club. There's been a few injuries and it's not the biggest of squads.
"But it's a lovely club and you never know, somebody fresh coming in could give the whole place a lift. (Caretaker-manager) Micky (Barron) has done his best, but he's also found it hard and I think now's the right time to bring someone new in."
Brown, 53, a former Hartlepool player, has confirmed his interest in the vacancy, while Craig Short, Livingston boss John Hughes and Middlesbrough coach Colin Cooper have also been linked with the post.