Coutinho scored a brace, with Firmino adding another in a 3-2 win over Kenny Jackett’s side at Melwood.
Klopp’s side also included Lucas Leiva, Dejan Lovren and Alberto Moreno, with the trio maintaining their fitness ahead of their inclusion in the German’s starting lineup for the trip to take on Manchester City next Saturday.
Kolo Toure stepped up his recovery from a hamstring injury to take a spot in Klopp’s back line, with Martin Skrtel away on international duty with Slovakia.
Joao Carlos Teixeira also featured, with the Portuguese looking to impress his new manager after featuring on his substitutes’ bench three times so far in the Premier League.
Perhaps most interestingly however, this clash was the first time Klopp could see 18-year-old summer signing Allan Rodrigues in action.
The Brazilian has returned from a successful loan spell with Finnish side SJK, after securing the Veikkausliga title—the first in the club’s history.
Allan is expected to leave on loan again in January, with clubs from Switzerland, Holland and Belgium believed to have registered their interest in signing the midfielder.
Klopp met with Allan on his return to the club at the end of October, and could plan a long-term role for the former Internacional youth at Anfield.
Sheyi Ojo and Sergi Canos, who have both made a brief return from their loan sides this week, both featured as substitutes, with Klopp looking to evaluate their progress.
Only nine senior players left the club on international duty this week, due to a number of injuries to Klopp’s squad.
The German will be utilising this 12-day period to continue his side’s development at Melwood.
Liverpool XI vs. Wolves: George; Alexander-Arnold, Toure, Lovren, Moreno; Lucas, Allan; Teixeira, Coutinho, Firmino; Sinclair
Substitutes used: Woodburn, Ojo, Dunn, Whelan, Ejaria, Canos, Kane