Assistant manager Pepijn Lijnders will take charge at Stamford Bridge on Monday (NZ time) in the absence of Klopp, who is isolating after reporting mild symptoms.
"Testing of the entire first-team set-up has revealed no further positive cases within the playing squad in addition to the three confirmed by Klopp on [Saturday]," Liverpool said in a statement.
"Three backroom staff members have returned suspected positive results, however."
The league has postponed 18 games, including Liverpool's Boxing Day clash against Leeds United, since last month due to Covid-19 outbreaks and injuries at several clubs, leaving sides without enough players to fulfil fixtures.
Liverpool were without the services of Virgil van Dijk, Thiago Alcantara, Fabinho and Curtis Jones in recent weeks after they were forced into isolation due to suspected positive Covid-19 tests. The quartet returned to training earlier this week.