The former Hoops boss was speaking after Scott Brown’s testimonial match, where O’Neill’s Republic of Ireland side squared off against the double treble winners.
He feels the hiring of Steven Gerrard as Rangers manager will see the Ibrox club improve dramatically on the park.
And if they do, Celtic will respond in kind.
He said: “It would be nice if Rangers could get stronger and that seems as if it might be on the cards. A good, strong Rangers side is good for the league and it would be remarkably good for Celtic.”
“There doesn’t seem domestically any resting of laurels here. If that competition gets stronger I think Celtic will rise to it.
“If they [Rangers] are in a position to delve into a transfer market and get some decent players then that will be a little reminder to Celtic.”