Derry City and Strabane District Council lent its support to the move after a meeting with the Derry Comhaltas on Tuesday.
An estimated 400,000 people attended the event in 2013 when it was brought to Northern Ireland for the first time.
It is the biggest festival of Irish music and culture anywhere in the world.
Evelyn Ni Dochartaigh is one of the organisers of the Fleadh. She said Â£1m in funding will be needed if the city is to host the festival once more.
"Within the euphoria of the 2013 fleadh there was widespread support that we would bid again. We put a proposal to the business and culture committee yesterday, it was unanimously supported but it does still need to be ratified by full council.
"The local authorities are crucial in this process, especially in terms of finances. We could do it for a million, that is what we are asking for, even though it cost around 1.6 million in 2013."
Ms Ni Dochartaigh also believes that any financial backing by taxpayers will be returned handsomely.
"What you don't want is people to say the first fleadh was great, this isn't so good. So we will tailor it to fit the cost. The economic benefits will outweigh that anyway, so it is a no-brainer."
Organisers who brought the All-Ireland Fleadh Cheoil to Londonderry will bid for the festival to return in 2017.