The rules were changed to allow an increase in the number of replacements when football returned amid the coronavirus pandemic in June 2020 but, when Premier League clubs voted on whether it should be kept permanently last season, it was rejected.
The matter was voted on three times last season and was refused every time, with the 14 votes needed to pass the rule never amassed.
However, that is to change, according to The Times, who are reporting that top-flight clubs are set to make a 'U-turn' and vote for the rule change.
Five substitutes has now become the norm in many other leagues across Europe, with the Premier League being the only major league in Europe to restrict the number to three, but the report goes on to say that there is 'high confidence' that there is now enough support for the alteration.
Some clubs wanted to continue with the five-sub rule ahead of the 2020/21 season, with the likes of Liverpool, Manchester United, Manchester City, Chelsea, Arsenal, and Tottenham all reportedly voting for the change.
Representatives of the division's 'Big Six', such as Jurgen Klopp and Pep Guardiola, have previously spoken of how they wanted more substitutions league.
However, there was strong opposition from the smaller teams in the division, who believed it would give an advantage to the teams that have bigger squads and would create an uneven playing field for sides with less depth.
During previously talk about the same rule change, a row erupted between Liverpool manager Jurgen Klopp and Burnley.
"The decision needs 14 votes to change it and that's something wrong," the Liverpool manager said in December.
"What we realised again in the managers meeting - and we know it has always been like that - is how 14 clubs make the decision to change.
"We have to put competition aside.
"[Five substitutes] is the right decision, especially in this moment, because you bring players back in this moment, after COVID infection or an injury, and because of the games they have to play you risk injury and they have to go out again, maybe after 60 minutes.
"That is a real problem. This wonderful game is so wonderful because usually the players on the pitch are in good shape, are well trained, are well recovered and go for it.
"That is why we love the game. Now the situation is much more difficult."
Taking aim at Burnley, Klopp added: "There is something wrong. Here is an example.
"With Burnley, I am not too sure how many of their players play international football.
"When our players play three games, they [Burnley] have no game.
"They have 38 Premier League games and three or four cup games, to make around 42 games a season.
"So we are talking about an issue which some clubs and players definitely have, but it is decided by the other teams and we make a competition of it.
"They say, 'well they are better than us', and that is a real problem. It's Premier League and can still cause us problems.
"How many games does a top-class player play? With the league, some cup games, Champions League, internationals - it's 50 games. Higher.
"The further you go the harder it is on players. You need luck in these moments and you should not need luck.
"We do not stop discussing it because if we don't discuss it, it just stays like this."