"Assistant manager Pep Lijnders will therefore lead the team for the 4.30pm GMT kick-off at Stamford Bridge."
No further Liverpool players have tested positive beyond the unnamed three previously confirmed by Klopp on Friday.
Despite distancing himself from suggestions the game could be in danger, Klopp this week described each new day as a "lottery" as he waited to discover if any of his squad had tested positive.
"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 Friday," the statement added.
"Three backroom staff members have returned suspected positive results, however."
If Klopp's positive test is confirmed, the German will also miss the League Cup semi-final first leg at Arsenal on Thursday.
The Premier League has been ravaged by Covid outbreaks since December, with Liverpool's game against Leeds on Boxing Day postponed due to virus issues suffered by their opponents.
In total, 17 English top-flight matches have been postponed due to Covid so far, while Arsenal manager Mikel Arteta missed Saturday's game against Manchester City after a positive test.
Liverpool stars Virgil Van Dijk, Fabinho, Thiago Alcantara and Curtis Jones all tested positive for Covid in December.
The Reds are one point behind Chelsea with a game in hand after losing their last league match at Leicester on Tuesday.
Liverpool trail Manchester City by 12 points, with two games in hand, following the champions' 2-1 win at Arsenal.