The midfield duo have been participating in full training ahead of the Group B fixture at Anfield after spells on the sidelines through injury.
However, the Reds will be without Naby Keita for Wednesday's 8pm GMT kick-off due to the hamstring issue he picked up during the draw with Brighton & Hove Albion on the weekend.
“Naby has a hamstring injury so will be out for a while," Jürgen Klopp told reporters on Tuesday. "Apart from that, Millie it’s clear [he won’t be involved] and the others who are out long-term will be out as well.
“Fabinho and Thiago trained completely normally and are in contention, which is good obviously. It’s very helpful and so we will see."
Mohamed Salah could make his 50th appearance for Liverpool in European competitions.
Atletico, meanwhile, are unable to call upon forward Antoine Griezmann and centre-half Stefan Savic, who are both suspended.
Diego Simeone also has Thomas Lemar and Marcos Llorente unavailable because of thigh injuries.
“We are not going to have Griezmann, Savic, Llorente or Lemar," Simeone said at his pre-match press conference. "They are out of the squad for tomorrow.
"But apart from those four players, we are still going to go there to fight and to compete – that you can be sure of."
Last time out
Liverpool 2-2 Brighton & Hove Albion (October 30): Alisson, Alexander-Arnold, Konate, Van Dijk, Robertson, Henderson, Jones, Keita, Mane, Salah, Firmino.
Atletico Madrid 3-0 Real Betis (October 31): Oblak, Trippier, Savic, Gimenez, Hermoso, Correa, De Paul, Koke, Carrasco, Suarez, Griezmann.