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The Denmark international, who played all 38 of Leicester's league games as the 5 000-1 outsiders won the title last season, picked up the injury against Copenhagen in the Champions League in November.
Schmeichel's fitness would be assessed before Saturday's against Manchester City but it maybe too early for the 30-year-old.
"Kasper is getting better and maybe he is ready for Bournemouth," Ranieri told the club website (www.lcfc.com).
"I think Saturday (against Manchester City) is too soon but let me speak to him on Friday. For me the possibility is no, but Kasper is a fighter. He could be (ready)."
While midfielder Danny Drinkwater will return on Tuesday from a three-game ban, Ranieri confirmed Nampalys Mendy will not start against Manchester City after the midfielder, on his return from an ankle injury, played the whole 90 minutes of Leicester's 5-0 loss to Porto on Wednesday.
"Of course, now he's made just a week or 10 days with us. I wanted to give to him just 60 minutes... I couldn't change any more and he played all the match. So, he needs to recover... He's available, but not to play from the beginning," he said.
Leicester are 16th with 13 points, two away from the relegation zone.
