National League side Chesterfield drew 3-3 with Championship club West Brom in the third round of the FA Cup last season, before losing the replay at the Hawthorns 4-0
The changes will also see the FA Cup fifth round restored to a weekend slot.
Changes have been triggered by pressure on the domestic calendar such as the expansion of European competitions.
It is not yet known when the changes could come into effect, though a new TV contract is set to commence in 2025-26.
However, the domestic calendar will feel extra pressure from next season when the Champions League and Europa League first phases expand to 36 clubs.
Subsequent alterations to the Uefa match calendar mean the opening phase will cover 10 midweeks rather than the current six.
With Fifa's international match calendar not due to change until 2026, when the four games currently played in September and October will run across a single 16 day window, it leaves a maximum of 12 spare midweeks for domestic matches to be played if clashes with European club competitions - which Uefa frowns upon - are to be avoided.
In their 'invitation to tender' statement released on Wednesday, the Premier League confirmed five midweek rounds per season would be part of their offer to broadcasters for the four-year cycle that starts in 2025.
That is one more than this season, when matches are due to be played in November, January and April, in addition to the Boxing Day slot.
With spare midweeks needed for matches that have to be rearranged due to clashes with the FA Cup sixth round and semi-finals, plus the EFL Cup final - which are all played on weekends used by the Premier League - there is not enough space for the domestic calendar to remain as it is.
BBC Sport understands the answer is set to come through alterations to the two cup competitions.
The FA could give up third and fourth round replays in exchange for a return to a weekend date for the fifth round of the competition for the first time since 2019-20.
While many observers felt the EFL Cup semi-finals had to be shrunk from their current two-legged format if the competition was to be retained, the loss of FA Cup replays for top-flight teams will be lamented by some, even though they were scrapped in 2020-21 and 2021-22 due to issues created by the coronavirus pandemic.
There were six replays in both the third and fourth round of last season's competition. The FA removed fifth round replays from the schedule in 2017-18.
The FA has declined to comment.
Its current broadcast deal with the BBC and ITV runs to 2025.
The EFL has just announced a five-year agreement with Sky that will end in 2029 and align with the next Premier League contract.
-- Courtesy of BBC Sport