The 21-year-old joined the Anfield outfit in a reported £8.5million deal in January, and has become an influential part of a squad that sits second in the Premier League table.
Coutinho - who has scored once in 10 league appearances this season - once more put in an assured display as Liverpool romped to a 4-1 triumph over West Ham on Saturday.
Rodgers revealed how he remains in close contact with Brazil coach Luiz Felipe Scolari after the pair worked together when the 40-year-old was a youth coach during the Brazilian's tenure as Chelsea boss.
And the Northern Irishman is hopeful Coutinho can join Liverpool team-mate Lucas in breaking into the international set-up ahead of next year's World Cup, which Brazil are set to host.
"He (Coutinho) plays like a street kid," Rodgers said. "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."
Liverpool have secured back-to-back Premier League victories, scoring nine goals in those fixtures, and lie five points adrift of table-toppers Arsenal.
