The Brazil international was a teammate of Suarez's for 15 months during their time at Anfield, before the striker forced through a move to Camp Nou in 2014.
Ahead of their reunion on the pitch, which has been delayed until next month due to a thigh injury picked up by Coutinho, Suarez told reporters: "As a former teammate, as a friend, I am very happy for him.
"I think he is going to contribute a lot to the team. Everyone knows the quality that he has - he has been in the elite group of players for many years."
Suarez scored his fifth goal in four outings on Sunday night as Barcelona eased past Levante 3-0 in La Liga.