The former Bournemouth boss is widely expected to be announced as Neil Lennon’s permanent successor.
Celtic released their season tickets this week, noting they had hoped to have announced a new boss before doing so.
Howe is still the strong favourite to be the man to tackle the challenge of competing with Rangers for the Premiership title but there appears to be five or six moving parts in the process.
Barnes, who managed Celtic between 1999 and 2000 expressed his intrigue at how the dynamic will work with the new boss.
With Dominic McKay taking over from Peter Lawwell as chief executive and a new sporting director expected, plus an expected revamp of the squad, it is a moment of substantial transition at the club.
"Like the right players looking for the right type of football to suit them rather than the club, I think Celtic and Eddie have to decide the kind of relationship they want,” Barnes told www.bettingodds.com.
“Is Eddie going to say, “I want to go and work at Celtic with what I have so I can make them better but I will need to be given time, it’s not going to work all of a sudden”? Or is he going to be like a big name European manager who’s going to expect to spend millions and get better players in?
“Because it’s Celtic and they have to challenge Rangers, they could go for a superstar manager and spend loads of money to get better players. That’s why you have to look at the dynamic of the club’s ambitions as well as the manager’s ambitions.
“I think working with what he has, Eddie will do a good job, but he’s not all of a sudden going to be better than Rangers.
“Rangers have got better players than Celtic and they’re in a better place, so the expectations of beating Rangers are maybe unrealistic.”
Celtic’s season will begin in less than two months with a Champions League qualifying tie on either July 20 or 21.