Burnley have requested for Tuesday's match against Watford to be postponed, with the Premier League set to make a decision on Monday.
The Clarets were successful in their appeal to have Saturday's match against Leicester postponed last week, due to a number of Covid cases and injuries in the squad.
Clarets boss Sean Dyche said at a news conference on Monday that they were down to 10 first-team players in training and "slightly worse off" than before the match against Leicester.
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It was the fourth Burnley match this season to be postponed due to Covid-19, but the first time the request had come from the Turf Moor club. They also had a game against Tottenham postponed because of heavy snow.
A league statement issued on Twitter read: "The Premier League has received a postponement request from Burnley relating to their home match against Watford due to be played at 7:30pm GMT on Tuesday 18 Jan.
"The Premier League Board will meet later today to review the application and inform both clubs and their fans of its decision."
Burnley's request follows Arsenal successfully asking for Sunday's north London derby to be postponed after losing players to Covid, injury, suspension and the Africa Cup of Nations.
There has been criticism levelled at Premier League teams over twisting the rules around postponements, which were implemented because of the coronavirus pandemic, to give them a competitive advantage.
The Premier League have no immediate plans to change any of their rules concerning postponing games in relation to Covid.
Neville: PL should force teams to play
Speaking on Friday Night Football before the north London derby had been postponed, Sky Sports pundit Gary Neville said:
"I honestly believe that all teams, not just in the Premier League but the EFL now, must be made to play their fixtures.
"If it was purely down to Covid in extraordinary circumstances where there was 10 or 15 players out, but we're now talking about teams for the last few weeks where there's no doubt they've been calling games off based upon whether they think they've got the best squad or team to win a game. It's got to stop.
"That's not a dig at Arsenal - I should've spoken about this three or four weeks ago.
"Manchester United and other teams have got 30 to 40 players in their squad - I'm not having they can't get 13 to 16 players together.
"For me, it [Arsenal's request] should be rejected.
"Without knowing the exact detail, unless there is an absolute load of Covid cases coming today at Arsenal, I feel having played last night at Liverpool, it has to stop now this and we have to make teams play."
Carragher: Young players should be given a chance
Also speaking on FNF, before a decision had been made on Arsenal's request, Sky Sports pundit Jamie Carragher said:
"I don't want this to be about Arsenal, it's about the Premier League as a whole. Every club has done this.
"No other league in Europe is doing this, certainly not in those big leagues. Bayern Munich played a 16-year-old in their last game and that tells you exactly where they are. Why can't we do that? Why can't the young players be given an opportunity in these circumstances?
"Everyone's in the same boat and I'm exactly with Gary. If it's an outbreak of Covid and it's decimated the squad I can understand that, but players being in the AFCON tournament and just normal injuries, that's got nothing to do with it.
"You've got U23 squads and younger players, and this is an opportunity where they can get a chance.
"I know there's a lot riding on Premier League games but at this moment there's no doubt teams up and down this country are taking advantage of the situation."
Which Premier League games have been called off?
Brighton vs Tottenham - Sunday December 12
Brentford vs Man Utd - Tuesday December 14 (now January 19, 8pm)
Burnley vs Watford - Wednesday December 15 (now January 18, 7.30pm)
Leicester vs Tottenham - Thursday December 16 (now January 19, 7.30pm)
Man Utd vs Brighton - Saturday December 18
Southampton vs Brentford - Saturday December 18; Southampton won re-arranged game 4-1 on Tuesday January 11
Watford vs Crystal Palace - Saturday December 18
West Ham vs Norwich - Saturday December 18; West Ham won re-arranged game 2-0 on Wednesday January 12
Aston Villa vs Burnley - Saturday December 18
Everton vs Leicester - Sunday December 19 and Tuesday January 11
Liverpool vs Leeds - Sunday December 26
Wolves vs Watford - Sunday December 26
Burnley vs Everton - Sunday December 26
Leeds vs Aston Villa - Tuesday December 28
Arsenal vs Wolves - Tuesday December 28
Everton vs Newcastle - Thursday December 30
Leicester vs Norwich - Saturday January 1
Southampton vs Newcastle - Sunday January 2
Everton vs Leicester - Tuesday January 11 (as above, this game had already previously been postponed from its original Sunday December 19 date)
Burnley vs Leicester - Saturday January 15
Tottenham vs Arsenal - Sunday January 16
What are the Premier League rules around postponements?
The 2021/22 Premier League handbook included Covid protocols and stated the Premier League's board will "only permit the rearrangement or postponement of a league match in exceptional circumstances".
The board make calls on a case-by-case basis, and by way of guidance the Premier League says permission for a postponement will not be granted if a club have 14 or more players from their squad list available.
However, after the postponement of a number of games in the weeks leading up to Christmas, a new Premier League guide explaining match postponement protocols was published.
And there, these factors are considered when deciding whether to postpone a top-flight game:
1) The impact of COVID-19 infections on a club's squad, as well as injuries, illness and those isolating, and the number of players available on the squad list and any Under-21 players with appropriate experience. Where a club cannot field 13 outfield players and a goalkeeper either from its squad list or its appropriately experienced Under-21 players, the match will be postponed.
2) The status of any COVID-19 outbreak within a club, including the number of individuals affected, the sequence and source of infections and their proximity to the match in question.
3) A club's ability to safely prepare its players in the lead-up to a match.
4) Medical advice as to whether there is any unacceptable risk to the health and safety of players and staff by playing the match.
5) Any advice from UK Health Security Agency and other public bodies.
6) Any other exceptional circumstances.