They've pledged €5m to the fund so far.
Offaly County Council is calling on the ESB to contribute €80 million the Just Transition Fund.
To date, the state-owned company has pledged €5 million to the cause, which independent councillor John Leahy says is just 0.5% of it receives annually from the PSO levy.
He says the county is set to lose out on €4.8 million in commercial rates when peat production stops, and the area is in desperate need of a cash injection.
Councillor Leahy has concerns over the distribution of funding for the Just Transition and feels the ESB has to play its part: