Cardiff City football club has backed Project Big Picture "in principle", saying finance has been an issue since the Premier League's launch in 1992.
The proposals, led by Liverpool and Manchester United, became public earlier this week and have split opinion.
Project Big Picture wants to reduce the Premier League from 20 to 18 clubs and scrap the Carabao Cup.
The EFL would also get 25% of all future TV deals, plus £250m.
However, it would also see more power transferred to the so-called 'big six' clubs in the Premier League.
It would need 14 of the 20 current top-flight clubs to vote in favour.
Fan groups of the 'big six' teams - Arsenal, Chelsea, Liverpool, Manchester City, Manchester United and Tottenham - have criticised the plans.
Some EFL clubs said support was "almost unanimous" among their member clubs - although that was later disputed.
Bluebirds bosses issued a statement which read: "Whilst there has been a negative perspective on the plan in the media on governance and control, it's easy to lose sight of the positives in the paper put forward to EFL Clubs.
"Since the formation of the Premier League in 1992 (when the remaining clubs in the Football League turned down an offer to link income to Premier League media rights), finance has been an issue.
"The link between the Premier League and Football League was further severed in 2000, when Football League clubs voted to go with ITV Digital instead of Sky, resulting in devastating consequences.
"Project Big Picture seeks to reconnect the link with the Premier League and guarantee future revenue streams in a marketplace which, domestically, is becoming stagnant.
"It will allow the EFL to benefit from the growing income generated by international rights which are currently unavailable to the EFL.
"The plan also includes a salary cap for the Championship to ensure a sustainable financial model is in place going forward.
In addition to increased and guaranteed income streams, the proposed project would help create a more level playing field in the Championship.
"It addresses the conundrum of parachute payments, which were originally brought in to provide a soft landing for clubs dropping out of the Premier League to pay off contracts of players who they could not move on.
"These payments have grown significantly over the years, affecting the integrity of the competition."
The Cardiff statement also highlighted other "positives" for the higher tiers of English football, including a fan charter to address fans' concerns, a chance to review the sport's governance and funding for the women's game.
"Discussions are at a very preliminary stage, but we would urge all parties, including the Government, to consider the proposals objectively. We hope they will then find a solution which benefits the game as a whole," the statement added.
Cardiff's intervention came after Football Association chairman Greg Clarke said a breakaway league was suggested "as a threat" by the organisers of Project Big Picture.
Meanwhile Aston Villa chief executive Christian Purslow says the proposals are "highly unlikely to get traction within the Premier League".
The 'Project Big Picture' proposals
- The Premier League cut from 20 to 18 clubs, with the Championship, League One and League Two each retaining 24 teams.
- The bottom two teams in the Premier League relegated automatically with the 16th-placed team joining the Championship play-offs.
- The League Cup and Community Shield abolished.
- Parachute payments scrapped.
- A £250m rescue fund made immediately available to the EFL and 25% of all future TV deals.
- £100m paid to the FA to make up for lost revenue.
- Nine clubs given 'special voting rights' on certain issues, based on their extended runs in the Premier League.