Thiago and Mane missed the Reds’ 7-2 thrashing at the hands of Aston Villa prior to the international break after both testing positive for Covid-19.
However, after completing their mandatory period of self-isolation, both men have returned to training ahead of the weekend’s trip to Goodison Park.
They are likely to be joined in the starting XI by Jordan Henderson, who overcame a hamstring injury to take a place on the bench at Villa Park almost two weeks ago.
Having stepped up his bid for match fitness by featuring for England in games against Belgium and Denmark, the captain is ready to play a full part in the Merseyside derby.
Matip is also an option for Klopp after recovering from a muscle problem, though he is considered unlikely to start due to a lack of match fitness.
Naby Keita’s involvement remains uncertain after the Guinean tested positive for coronavirus while on international duty – the results of a secondary test have yet to be public.
Meanwhile, Klopp has a tough decision to make over the involvement of his two Brazil internationals, Roberto Firmino and Fabinho, after they were both involved in energy-sapping trips to South America.
The boss must also contend with the absence of his injured first-choice goalkeeper Alisson Becker, with Adrian San Miguel set to continue as stand-in.
Predicted Liverpool XI to face Everton (4-3-3): Adrian; Alexander-Arnold, Gomez, Van Dijk, Robertson; Fabinho, Thiago, Henderson; Salah, Minamino, Mane.