Ten Premier League clubs voted against allowing five substitutes in the top flight this season at a shareholders' meeting on Thursday, the PA news agency understands.
Burnley, Aston Villa, Crystal Palace, Fulham, Leicester, Leeds, Newcastle, Sheffield United, West Ham and Wolves are understood to have opposed allowing two extra changes per match.
Advocates of allowing five substitutes include Liverpool and Manchester City managers Jurgen Klopp and Pep Guardiola, who argue it is vital to protect player welfare in a campaign which has been compressed due to the coronavirus pandemic.
West Ham's decision to vote against it is particularly surprising after their manager David Moyes said he had changed his mind on the issue.
The temporary amendment to the laws of the game to allow five changes was approved by law-making body the International Football Association Board (IFAB) earlier this year following a proposal from world governing body FIFA.
Premier League clubs did vote to allow five substitutes when the 2019-20 campaign resumed over the summer but two further votes to keep it in place for 2020-21 failed, prior to Thursday's third vote.
A 14-club majority would be necessary for the motion to be carried.
The Premier League is an exception among major European leagues in only allowing three substitutes, with the EFL also voting to permit five last month.
Five substitutes will be allowed in Football Association competitions such as the FA Cup, and the governing body's chief executive Mark Bullingham spoke of his "surprise" at the Premier League's failure to adopt the rule change.
"I think when we started off at an IFAB level we fully expected all of the leading leagues to sign it off for the reason of a very congested season with a lack of a pre-season, and we were surprised that the Premier League hasn't signed it off," Bullingham said on Wednesday.
"The reason we want it in our competitions is the reason most other leagues around the world have applied it – that is, for player welfare.
"Would we prefer it if the Premier League brought in five subs? Yes, we would prefer it. Is that our decision? No, it's not."
On Wednesday IFAB extended the amendment through to December 2021 for domestic competitions and to July 2022 for internationals. It may decide to extend the domestic amendment to July 2022 when its AGM takes place in March next year.
The Premier League has agreed to apply to take part in a trial allowing the use of two additional permanent concussion substitutes.
The trial could start as early as next month, and follows an announcement from the FA that it had also applied to trial the same protocol in the men's and women's FA Cups, the Women's Super League and the Women's Championship.
In a major boost to the league's finances, it also announced a new television deal with beIN SPORTS for the Middle East and North Africa region for the 2022-25 period.
It is understood the deal is worth 500million US dollars (over £367m) in total, which keeps it at around the same level as the previous contract despite the added economic pressures of the pandemic.
