The Premier League side claimed a 2-0 win over AC Milan in Charlotte on Saturday as they reached the International Champions Cup final to face Manchester United.
Sturridge sat out the clash due to a hamstring injury and has now headed back to Anfield, but Rodgers expects the striker to be fit for the clash against Borussia Dortmund on August 10.
"Dan has flown back to the UK," Rodgers told reporters. "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."