not holding the event at all that year as a last resort.
Dr Evans said: "We understand the financial problems facing local government.
"But at the same time we are disappointed that after so many years discussing the issue, Flintshire council cannot see the way forward to doing something that I think they would wish to do."
The eisteddfod's council has granted permission for the management board to consider all options and report back to the next council meeting on 25 June.
Before the meeting, Elfed Roberts, director of the National Eisteddfod, mentioned that talks had been held with the Wales Local Government Association (WLGA).
"Since last September we have been in talks with the association to see if all of the 22 local governments could contribute towards the eisteddfod," he said.
The eisteddfod, an annual celebration of music, dance, poetry, and art, has been held in Liverpool three times before - in 1884, 1900, and 1929.
Traditionally, the festival alternates between north and south Wales each year and this August it will be hosted by the Faenol estate in Gwynedd.