Liverpool have re-opened their training ground after a two-day shutdown following an outbreak of Covid-19 among players and staff.
"Multiple" cases were reported among a squad stretched by players leaving for the Africa Cup of Nations.
Assistant Peter Krawietz is in charge in Klopp and Lijnders' absence.
The 50-year-old German, who has worked alongside Klopp for more than 20 years, is leading preparations for the FA Cup third-round tie against Shrewsbury Town at Anfield on Sunday.
Liverpool will be without Mohamed Salah, Sadio Mane and Naby Keita, who are representing Egypt, Senegal and Guinea respectively at the Africa Cup of Nations.