McCann, in an interview given to mark the anniversary of his rescue of Celtic from financial ruin, said: "I would like to see the EPL expand and include Celtic. I think it could and should happen. It would triple the size of the club in financial terms, overnight."
In Barcelona, meanwhile, Lawwell was elected to serve on the executive board of the European Club Association. The ECA, which replaced the G14 group of top clubs in 2008, is recognised by UEFA and FIFA as the voice of 214 clubs from 53 nations.
Board members include chairman Karl-Heinz Rummenigge of Bayern Munich, AC Milan's Umberto Gandini, Edwin van der Sar of Ajax and Ivan Gazidis of Arsenal. Its mission statement says it exists to ensure that "club football is recognised by decision-makers as the most direct link to the fans and their communities".
A growing element of the ECA seeks to change the league model of club football where teams must only play in the country of their national association.
Lawwell said last night: "European football is an ever-changing landscape and, from the perspective of Celtic, it is vital that we ensure we are at the heart of the action and at the centre of discussions regarding the development of the game. As we look to the future, I look forward to representing Celtic, Scottish clubs and the other clubs in Europe to ensure that the voice of these clubs and their supporters is heard."
The chief executive has long pushed for Celtic to play in a league outside Scotland and McCann, who led the club from the financial abyss in 1994, lent his weight to this campaign.
He said: "The EPL now dwarfs Scottish football financially and makes Celtic's progress a daunting challenge. Nowadays, supporters want the best, and that is impossible in Scotland generally with too many small clubs. This is obvious."
McCann was also questioned on whether he felt his strategy in the 1990s was vindicated by the financial problems at Ibrox, forcing Rangers into administration and subsequent liquidation.
McCann was criticised for perceived parsimony against the free-spending regime under Sir David Murray at Ibrox. However, in a climate where Rangers continue to make headlines over the state of their finances the former majority shareholder of Celtic declined to criticise directly the club or any individual.
But he said: "Everybody wants to win all the time but not everybody can. Football clubs should be ambitious but have to manage risk. Many have not done this well." He added: "And there is great temptation to do expensive, short-term deals. I worry about the effect of current owners who 'do not care what it costs' such as at Chelsea and Man City on the overall game."
McCann will return to Celtic Park in August to unfurl the league title flag with Celtic cruising towards a third successive championship. He was booed when he was at a similar ceremony in 1998.
Asked about how he felt about this reception, he said: "I think this was over-publicised. It was disappointing but did not bother me greatly. People pay their money and have the right to applaud or boo as they wish."