Neil Lennon has taken charge on a temporary basis and the former Northern Ireland international, who is a firm fans' favourite, began his reign with a 3-0 win over Kilmarnock on Saturday.
The 46-year-old Manchester United great has been biding his time for the right opportunity since leaving City according to Bowen, and he is flattered Hughes has been linked with the vacant Parkhead post.
"We're not in the business of just going in and getting a fat cheque and thinking 'Well, if things go wrong we'll be out in a year's time and we'll go somewhere else'," Bowen told the Daily Record.
"Mark has always said it has to be the right vehicle, the right situation. He's always been a manager or coach who wants to go in and build a place and make a difference long term.
"It's what we did with Wales and Blackburn and we were in the process of doing at Manchester City.
"It seems to be the natural thing at the moment that Mark is linked with any vacant manager's position.
"His talents are widely recognised and since City we've been waiting for the right opportunity.
"In that sense, I suppose we were expecting this speculation and it's a pleasant expectation to see that he's been linked with the Celtic post.
"Mark's credentials are there for all to see."