The Premier League side claimed a 2-0 win over Milan in Charlotte on Saturday as they reached the International Champions Cup final.
Sturridge sat out the clash due to a hamstring injury, and the England international headed back to the United Kingdom.
Rodgers said he expected the 24-year-old to be fit for the clash against Borussia Dortmund on August 10.
"Dan has flown back to the UK," the Northern Irishman said.
"He wasn't going to be ready for the game on Monday - but there's no concern there, he'll be ready for Borussia Dortmund at the weekend.
"It was just best to get him back early, back to the training ground so he could get some treatment there.
"He had a really, really slight feeling in his hamstring. It's nothing major."
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