Talks between the governing body and clubs began on Thursday and the Derry board said it hoped to address the matter during further talks this week.
A club statement also said that the Premier Division is likely to restart in mid-August, with next month’s four-team tournament now not taking place.
“The FAI has recognised the need to provide financial support,” Derry said.
In the statement, the club said the board wanted to keep supporters informed of how the discussions between the FAI and the clubs in the Premier Division and First Division were progressing.
“This support is to compensate clubs for having to play games at designated stadiums and behind closed doors,” the statement continued.
“The Derry City board are not yet convinced that the proposed distribution is equitable.
“Derry City is one of only three clubs who have kept their staff and players on full salary.
“That effort and commitment has not been properly recognised in the proposed distribution of financial compensation.
“Negotiations will continue this coming week and the Derry board will continue to be constructive and supportive in the difficult circumstances that have arisen because of the pandemic.
“Hopefully, those efforts will be properly recognised in the continuing negotiations.
“We will fully inform our supporters when negotiations have concluded.”
The Candystripes and the other three League of Ireland teams to have qualified for Europe – Dundalk, Shamrock Rovers and Bohemians – were due to play in a four-team tournament in July.
That has been cancelled due to the pending restart of the league in mid-August.
Players and staff from all four clubs have undergone a series of COVID-19 tests, all of which have returned negative.