The aim is to hold him back for Sunday's Merseyside derby at Everton, who are four places above their neighbours. But Rodgers will be happy with England naming him on Thursday for their final Euro 2016 qualifying matches in a week's time.
"He won't be involved in the (Sion) game," Rodgers told a pre-match news conference. "We'll keep him fresh for the weekend. He's still building his way towards fitness."
The England striker missed six months of last season in all with calf and thigh injuries and then the first five league matches of the new campaign.
In his second game back last weekend he scored twice against Aston Villa, delighting Rodgers with the way he combined with new signing Danny Ings.
"If we can keep him fit, there's a real good combination there. It was a real threat," the manager said.
"Our approach to this game will be how it's been in the competition so far. It's an opportunity for players on the fringes," Rodgers added, confirming that 18-year-old midfielder Jordan Rossiter will feature.
He made his debut in a 1-1 draw with Bordeaux in the opening Group B game. On the same day Sion beat Rubin Kazan 2-1 to top the table.
"It's a game where we're going to need to be patient," Rodgers said. "Sion sit deep and then play a counter-attacking game."
(Reporting by Steve Tongue; editing by Sudipto Ganguly)
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