Bell and Coleman, who have been at the Crown Ground for 10 years, were linked with the Tranmere job following Ronnie Moore's departure.
The pair were eventually overlooked, though, and Bell has underlined their committment to Accrington.
"I was asked the question, 'Would we be interested?' I said, 'Of course'. It's a big job so it would have been a step up," he told the Lancashire Telegraph.
"We have never stood in the way of players when they have had the chance to step up. It wasn't to do with the finances, it's like anyone in their job, if you get the chance to move to bigger organisation, you're interested.
"But we're not looking to jump ship. Me and John will always give everything to Accrington, as we always have."