The clubs have expressed their concerns that teams that are relegated from the Premier League will have too great a financial advantage.
The concerns were expressed at a meeting of the 24 second-tier clubs on Wednesday after they were presented with the Premier League's proposals for parachute payments to be £23million for the first year after relegation.
Clubs in the Championship not receiving parachute payments would get just £2.3million.
The outcome of Wednesday's meeting was inconclusive, with the Football League board asked to come up with a range of options and to continue discussions with the Premier League, club sources confirmed.
The increase in parachute payments from £16million is because of the rise in the Premier League's TV rights from 2013-16 - and it effectively decides on the level it pays.
The Football League clubs were informed of the proposed rises in a letter from chairman Greg Clarke.
The proposals is for relegated clubs to receive £23million in the first year, £18million in the second and £9million in years three and four. It would mean a possible total of £59million over four years compared to the maximum now of £48million.
The new offer of solidarity payments for League One clubs are for £360,000 and £240,000 a 6.6% and 5.4% rise respectively.