The proposal is part of a package of solidarity payments for Football League clubs that is being debated, with a decision due at the Premier League clubs' AGM in June.
It is understood however that any change would not go through without the consensus of the Football League.
Inquiry: Portsmouth's future is under threat after their dismal season
The parachute payments, aimed at softening the financial blow of relegation, are due to rise from £12million a year to £16million from this summer.
The one worry about extending the payments is that they could serve to increase the advantage that relegated clubs hold over their rivals in the Championship in terms of being able to guarantee higher salaries to players for a longer period.
The Premier League agree a package of solidarity payments to the Football League over three years.
The 2007-10 package saw more than £90million handed over including £5.4million for youth development.
Money for Championship clubs varied depending on how many were in receipt of parachute payments - those that had made an instant return to the Premier League no longer received them and the money was distributed across the rest of the Championship depending on where they finished in the league table.
League One clubs received £103,480 each, with £68,987 going to League Two clubs.
Portsmouth set for new owner as Rob Lloyd fronts deal for mystery investorCharles Sale: Labour and Tories wishing on a tsarRedknapp: Ignore the idiots, I made Portsmouth a transfer profitSpurs boss Harry Redknapp faces hot reception on return to Portsmouth