A club statement said: "The Reds have formally requested to the EFL that the fixture is rescheduled after further suspected positive tests were registered among players and staff, allied to other factors impacting selection, including illness and injury.
"In response, the club halted preparations at the AXA Training Centre, meaning Tuesday's first-team training session was cancelled.
"Among the considerations which led to today's application to the EFL is the need for travelling supporters to be given as much notice as possible of any potential postponement."
Manager Jurgen Klopp and three first-team players missed the 2-2 draw with Chelsea after returning positive tests, and the extra challenge of the Africa Cup of Nations has seen them lose more squad members.
The second leg of the League Cup tie is scheduled to take place just a week later on January 13, leaving little room for rescheduling.
An EFL spokesperson said: "The League has this evening received a request from Liverpool to postpone Thursday's Carabao Cup semi-final first leg versus Arsenal, which will now be considered in accordance with the competition rules as set out at the start of the season alongside information submitted by the Club.
"We will look to confirm the League's position as soon as possible once the circumstances have been fully reviewed."
Klopp was already set to miss the first leg due to self-isolation rules, with Alisson Becker, Roberto Firmino and Joel Matip also in quarantine.
The start of AFCON has seen Liverpool's list of absentees increase by three with crucial duo Mohamed Salah and Sadio Mane heading to Cameroon along with midfielder Naby Keita.
The Reds are also without Thiago Alcantara, while squad players Takumi Minamino and Divock Origi remain doubtful.
Thiago has also already missed game time with the virus, alongside Virgil van Dijk, Fabinho and Curtis Jones.
If the match goes ahead, Klopp's assistant Pepijn Lijnders will lead the team for the first leg having taken the German's spot on the touchline at Stamford Bridge, while Mikel Arteta is due to return to the Arsenal dugout after also testing positive.
The new Omicron variant of the COVID-19 virus has been causing havoc in English football, with 18 Premier League games postponed already this season.
However, positive tests across the division have decreased for the first time in eight weeks, with 19 cases down from the previous week's total of 103.