The Brazilian handed in a transfer request last month in the hope of pushing through a move to Barcelona, who reportedly tabled three bids, one of which is said to have rose to £114m.
However, Liverpool stood firm in their stance that the playmaker is not for sale and he has now been included in Klopp's Champions League squad for the upcoming campaign.
Aldridge believes that the 25-year-old will be part of Liverpool's squad for this Saturday's clash against Manchester City, but does not expect him to start.
"Look, forget about all the furore over Philippe Coutinho over the past week - he should be back and that will be a massive boost," Aldridge wrote in the Liverpool Echo.
"He will probably be in the squad and it will probably be on the bench, but that's the right call for me. At the moment, the lads in the starting line-up are playing so well, he needs to wait. That's how it should be, too."
The Merseyside are unbeaten in five games in all competitions so far this season, and they have won their last four on the bounce.