The Northern Irishman, who knows Brazil coach Luiz Felipe Scolari from his time at Chelsea, hopes to see the youngster join Lucas Leiva in the Selecao's summer plans
The 21-year-old joined the Reds in January and has become an influential part of a squad who sit second in the Premier League table, putting in an assured display in Saturday's 4-1 triumph over West Ham.
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"He plays like a street kid," Rodgers enthused of the midfielder. "He plays like a boy but his performances are like a man. He's a brilliant player.
"I am constantly on to Scolari about him because I know him from my Chelsea days. Brazil do have a raft of talent but Coutinho is a really exceptional player for his age and, hopefully, he might get into the squad.
"Lucas has got into the squad, which is great, so hopefully Philippe can follow suit and join him on the international scene.
"It is more difficult for his position and there is a lot of competition and players, but he is at that level."