Celtic are currently on the look out for a new manager, after parting company with Ronny Deila.
Hartson has been one of the most outspoken critics of current Celtic boss Ronny Deila.
The former Bhoys striker has stressed for a long time that he felt Deila was not the right man for Celtic, and he made that point to O’Neill.
“I spoke to Martin O’Neill the other day discussing how Celtic make the same mistakes and concede the same goals all the time,” Hartson said.
“I said to him, ‘You’d have had us out training for six hours if we’d defended like that’. He would have rectified the problem and if you didn’t do it then he’d replaced you with players who were good enough.
“Martin didn’t say too much but he said, ‘I can see where your point is coming from John’.”
Hartson has got his wish for a change of manager at Parkhead, as Celtic confirmed that Deila was set to depart at the end of the season yesterday.
Deila’s current deal expires at the end of the campaign, and he will not be offered new terms, bringing his two year stay to an end.
O’Neill, who currently manages the Republic of Ireland, has been touted as a potential candidate to takeover, but he is not one of the favourites.
At the moment, David Moyes is considered the most likely candidate to get the job at Celtic - with the likes of Roy Keane and Michael O’Neil close behind.
Hartson has told BBC Sport that he would like to see Neil Lennon get the job.