The 20-year-old Brazilian arrived from Inter Milan for £8.5million in the final few days of the transfer window.
However, he has only just spent his first few days training at Melwood after returning to Italy to finalise all the necessary aspects of the move.
It was not an ideal introduction either as many of the players were away on international duty after midweek games so he had a "bridging session" on Thursday and took part in his first full training the following day.
Unlike fellow January signing Daniel Sturridge, who came in at the beginning of the month from Chelsea and made his debut a few days later in the FA Cup, Coutinho is likely to be introduced gradually having had a recent injury at Inter.
"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."
Rodgers insists the gap between themselves and fourth place is not insurmountable before the end of the season but knows his side will have to show a level of consistency not seen for some time.
He is pinning his hopes on a recent upturn in their home form, which has seen them win three successive matches and score 12 times, and the boost in confidence from successive draws with Arsenal and Manchester City.
"In terms of the performance level I can only be happy after those games," he added, ahead of tomorrow's visit of West Brom.
"Offensively we were very good - we were obviously disappointed with the goals we conceded - and we felt we should have taken more points.
"The confidence in the team is the real important factor for us - all players are wanting the ball, working very hard.
"We went to Manchester City and had 21 shots at goal so we look like we are always going to score and there is a real determination in the group to finish the season well.
"West Brom have not started the year as they would have wanted but it will be a difficult game for us on a Monday night as Steve (Clarke) has done an excellent job there.
"But at Anfield there is a greater confidence that we have in terms of our game and that is something we want to continue through to the end of the season."