The Englishman is being touted as a potential candidate to replace Neil Lennon, who left Parkhead this week.
And similar to Brendan Rodgers, O'Hara thinks Dyche could cement his reputation as a top manager by winning titles in Scotland.
"He has kept that club on a tight budget and run that football club extremely well.
"He has kept them in the Premier League all these a years, they are always a great side and tough to beat.
"Has he taken that club as far as he can take it? They are never going to win anything.
"They will always be a Premier League outfit with Sean Dyche in charge but is he ever really going to stamp his authority as a top class manager?
"You look at Brendan Rogers who went to Celtic, even though he was manager of Liverpool, but he went to Celtic and it put him on a platform as a top class manager because he went there and won things.