Both the Guardian and the Daily Mail report that the idea is to be part of the discussions with new FA chairman Greg Dyke, who is looking to overhaul the English game.
The clubs believe that it could help the English national team improve as they could use their feeder clubs to give young English players on their books a chance to play competitively at a senior level.
At the moment clubs send players out on loan for this purpose, but with feeder clubs they could more closely monitor their development and style of play.
Such systems are already common on the continent. Many of Barcelona and Real Madrid's star players - including Lionel Messi, Xavi and Juan Mata - began their careers at what are effectively the reserve sides, Barcelona B and Real Madrid Castilla respectively. Both currently play in the Spanish equivalent of the Championship, and indeed Pep Guardiola also started his coaching career with the B team.
It may not be a question of starting up a B team, though: cash-strapped teams in lower leagues could be taken over wholesale by Premier League clubs and used as feeder sides - though existing fanbases of lower league clubs would unlikely be happy to see their team acting as a farm for another team's players.
Yet turning the reserve sides into branded B teams, such as they have in Spain and Germany, would mean other clubs would lose their spots in the Football League.
In a hard-hitting maiden speech as Football Association chairman last month, Dyke made it clear that he believes the English game is not in a healthy state.
He reeled off a number of statistics, all of which underlined just how few English players are starting regularly in the top flight.
He spelled out his grim diagnosis by telling a captivated audience in central London: "The situation is very serious.
"English football is a tanker which needs turning.
"And we all have a responsibility to do our best to reverse this frightening trend because if we fail we will be letting English football down and we will be letting the nation down."
Q&A - FEEDER CLUBS
How would feeder clubs work?
In one of two ways. Premier League sides might be able to enter their reserve teams into the main league system, or else buy out a lower league side and take over completely. The feeder teams would be fully owned by their parents, but succeed or fail on their own merits.
Would they play in all competitions just like a 'normal' team?
Yes: to all intents and purposes they are normal clubs with the same status and opportunities as any other. There would be no point running things otherwise, considering that it's all about giving players experience.
Wouldn't that lead to some strange anomalies?
Absolutely. In Spain, for example, Real Madrid Castilla made it to the final of the Copa del Rey back in 1980 - where they faced Real Madrid! The 'senior' team won 6-0.
How about promotion? Could there one day be two Chelseas or Uniteds in the Premier League?
That's the sole limitation on the feeder teams: they cannot play in the same division as their parent club. Again in Spain, both Real Madrid's and Barcelona's have earned promotion to the top flight, but been denied the chance to move up. Theoretically they could go up, but only if the parent club happened to be relegated in the same season.
Given the wealth of talent at the Spanish clubs, that has led to some interesting anomalies: Real Madrid Castilla and Barcelona B have both won promotion to the Spanish top flight on occasion, but cannot move up a division according to league rules. The most recent exanoke was 2010-11, when Barcelona B were denied a spot in the play-offs despite finishing third in the table.
There's another potential twist as well: should the parent club get relegated to the division in which the feeder club played, the feeder club would also have to drop down a division to avoid a clash.