The 20-year-old Brazilian midfielder joined the Reds from Internazionale for £8.5million at the end of the transfer window but has only spent the last few days training at Melwood after returning to Italy to finalise the move.
Unlike fellow January signing Daniel Sturridge, who joined from Chelsea and was put straight into action, Rodgers says Coutinho will be eased into the Liverpool starting XI but once he is up to speed the manager expects him to play a significant role.
"He's a young player I've got very high hopes for but Daniel was ready to come in and play - we'll see how young Philippe goes," said Rodgers.
"He was with the medical team with Milan and he has come here and we have assessed where he is in terms of his fitness.
"He trained with the group on Friday and we'll observe him and see where he's at but competition for places is what we want, that was the whole idea of bringing him in.
"He's a top young player with big experiences and bringing him into the group adds that competition.
"There's no doubt that the team who have been involved in the last couple of games have been exceptional but it's very important that we've got players in the side who are fighting to get into the team.
"The key for us has always been to build a competitive squad that would enable us to challenge. That will keep us going and allowing us to develop."
You can only watch the best Barclays Premier League coverage here on Sky Sports. Watch Liverpool v West Bromwich Albion exclusively live on Sky Sports 1HD, 3D and Sky Go from 7:00pm on Monday 11th February. Click here for more details