The proposals will be discussed at the Premier League shareholders' meeting on Wednesday, according to The Times.
The changes are aimed at easing the congested football calendar for Premier League sides, while distributing more funds to the English Football League.
One notable proposal is to scrap FA Cup replays for third and fourth round matches from 2024, a move which would require approval from English football's governing body.
Quarter-final replays were first scrapped after 2016, while fifth-round replays were shelved in 2018.
Another radical proposal is to make major changes to the League Cup, currently known as the Carabao Cup for sponsorship purposes.
The plan would see the clubs involved in European competition field their U21 sides in the Cup instead of their senior teams, or not take part in the competition at all.
The last nine winners of the League Cup have been one of the 'Big Six' Premier League clubs who regularly compete in European competition, with last winner outside of this group being Swansea back in 2013.
A final decision on the proposals is unlikely to be made this week, according to the report.
But if they are given approval by Premier League clubs and the FA, it is believed they could come into force for the start of the 2024-25 season.
That would coincide with the changes to the Champions League format, which will see teams play four more group matches than is currently the case.
The discussion around the congested football calendar was reignited last month after Chelsea co-owner Todd Boehly suggested the Premier League could stage a North v South all-star match.
Boehly claimed the match could help raise funds for the Premier League and the English Football League.
However, his proposals received widespread criticism, with Liverpool manager Jurgen Klopp among those opposed to the plans.
"When he finds a date for that he can call me," said Klopp.
"In American sports these players have four-month breaks. Maybe he can explain that.
"I'm not sure people want to see that - [Manchester] United players, Liverpool players, Everton players all together. North-east too, so Newcastle.
"It is not the national team. All the London guys together, Arsenal, Tottenham, great. Did he really say it?"
Klopp added: "Does he want to bring the Harlem Globetrotters as well?"
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