The Brazilian playmaker suffered a high ankle strain in Liverpool's 3-3 draw with Everton on November 23 and was unable to train before Sunday's 3-1 defeat at Hull City.
Coutinho came on as a 66th-minute replacement for Raheem Sterling at the KC Stadium, and Rodgers said on Monday that the 21-year-old came through the game unscathed.
"Philippe will be fine," Rodgers said on Monday, adding that he was hopeful on the fitness of defender Kolo Toure, who suffered a hip injury at Hull.
"He (Coutinho) has had no further reaction from the game yesterday. He's trained this morning, so all being well he'll be fit.
"We'll assess (Toure) in the next 24 hours, but hopefully he should be available."
Rodgers was hit with the news that striker Daniel Sturridge faces an absence of between six and eight weeks with an ankle injury over the weekend.
And the Northern Irishman is confident he will be backed to sign players in the January transfer window, providing they were of a sufficient calibre to improve the side.
"I always look at the bigger picture and the bigger picture is pretty bright. I'm really only focused on where we are at this moment," he added.
"Every window will be exactly the same. If there's a player we think we can improve our squad, and in particular our team, we will be in a position to go out and try to get that player."
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