O'Neill is confident that Rodgers can continue to make history with the Glasgow outfit after securing a monumental 'double treble' this season. The Northern Irishman spoke to reporters at Celtic captain Scott Brown's testimonial match on Sunday.
He said: ''I think getting to a European final can be done again. I don't think it's impossible. Brendan is dominating Scottish football now and Celtic have been very strong. The next step now is to try to achieve success in Europe.''
O'Neill also praised the newly appointed Steven Gerrard, who will take over at Celtic's rivals Rangers, and hopes that the former Liverpool legend can shape Rangers into a side capable of contending Celtic for titles.
He noted: ''It would be nice, imagine me saying this, if Rangers could get stronger. That seems as if it might be on the cards and a good, strong Rangers is good for the league. And actually, it will benefit Celtic to get stronger in Europe.''
''Personally, I think Steven Gerrard is a really good appointment. There is always a viewpoint in terms of inexperience but he is bringing Gary McAllister along, who has lots of experience.''
''The combination should be good and I think he will be really good for Rangers. Steven was a brilliant player and that doesn't always materialise into being a brilliant manager. But he has all the attributes and he wants to have a go. And why not?''
O'Neill concluded: ''If Rangers are in a position to delve into the transfer market and get some decent players, it will be a reminder to Celtic.''