The Northern Irishman won his first Clydesdale Bank Premier League title as Celtic manager last week and hopes to take the next step towards a double in Sunday's William Hill Scottish Cup semi-final against Hearts at Hampden. However, the former Parkhead skipper is confident he can go even higher with Celtic if given time.
"My ambition is to win the Champions League," Lennon told a number of newspapers. "Here or anywhere, that's my ambition. I never reached those heights as a player and I may not reach those heights as a manager - but that's what I'm aiming for."
He added: "You must keep a vision within your head and try to do everything you can to achieve it. Is it possible to win it here? Yes, definitely.
"It might not be possible to do it in a year or two years' time. But if we can consistently get in the Champions League and gain the revenue from that then we can build a team that could challenge.
"It's an ambition, that's all. I'm not saying: 'I think we are going to win the Champions League', but we have to have ambitions for it.
"I'm not the oracle - I don't have all the answers. But every now and again the Champions League does throw up a surprise package."
The former Leicester player went on to cite Jose Mourinho's Porto side of nearly 10 years ago as an example to follow.
He added: "Look at 2004 when Porto and Monaco got to the final - you would never have envisaged that. That was a great Porto team that beat us the year before in the UEFA Cup Final.
"I'm not saying this team is anywhere near our 2003 team yet but they have the potential to achieve something and we are hoping Europe is going to be the marker."
Source: PA
Source: PA