"We wish to clarify certain issues. There is certain unhappiness about a four-year parachute payment which some of the clubs think could distort competition. We've got to engineer a consensus."
BBC sports news correspondent Dan Roan said: "On the face of it the Premier League's proposals, including a doubling of the parachute payments to relegated clubs, seems very generous.
"But the Football League, especially those in Leagues One and Two have two concerns - firstly that it will, in time, create a 'second' Premier League in all but name, and secondly that it will threaten the Football League's sovereignty by forcing through rule changes."
Under the proposed extension of parachute payments, clubs would receive £16m in each of the first two seasons after relegation from the Premier League, and £8m in years three and four.
There is no appetite for a breakaway - we need to sort this out between ourselves
Unnamed Championship club chairman
Championship clubs not in receipt of parachute payments have received £830,000 over each of the last three years. Under the current proposals, that figure would rise to £2.2m per season.
However, League One and Two clubs would receive only modest increases, earning £325,000 and £250,000 respectively.
One Championship club chairman told the Press Association: "Understandably the Championship clubs were in favour because it means a lot more money for them, but the League One and Two sides are worried it will create a big gap.
"But there is no appetite for a breakaway - we need to sort this out between ourselves."
Meanwhile, a League Two chairman said the proposals "effectively create a Premier League Two by stealth, locking many of us out."
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