The culture year has so far attracted 1.5 million new visitors to the city
Liverpool is bidding for £3m of funding to build on its success as European Capital of Culture.
The city council is backing an application for North West Development Agency and European Regional Development Funding for 2009-2012.
It wants to create an "enhanced programme of cultural events over the next three years" to act as a lasting legacy to the 2008 culture year.
The Capital of Culture year has so far attracted 1.5 million new visitors.
The council says it has also generated national and international publicity for the city worth more than £70m.
Highlights have included the Liverpool Sound concert at Anfield featuring Sir Paul McCartney, the Tall Ships festival and the recent visit from La Machine, the spider street theatre performance through the city centre.
It is absolutely crucial that we build upon the amazing achievements of 2008
Council leader Warren Bradley
Council leader Warren Bradley said: "Much of the success of this year has been down to great partnerships and teamwork involving many of the city's cultural institutions and other organisations.
"A proposal is now under active consideration to secure further funding to put on an enhanced programme of cultural events over the next three years to build on our legacy of achievement," he said.
"We have been talking to chief executives of the other city region boroughs and have an ongoing dialogue with the major cultural and arts institutions.
"I also want to broaden our engagement, particularly in the fields of sport and young people.
"It is absolutely crucial that we build upon the amazing achievements of 2008 and securing additional funding will enable us to build a programme worthy of a major European city like Liverpool."
A bid for more than £3m is being prepared and has already passed its initial appraisal by the Mersey Partnership.