The midfielder struck against Manchester City in New York on Wednesday night but only notched five times last season, with his manager hoping he now hits double figures
The Reds got the better of Manchester City in the International Champions Cup on Wednesday, winning 3-1 on penalties, with the England international netting in normal time.
It was a rare goal for Henderson, who had only managed a total of five in all competitions last season, but Rodgers has challenged the 24-year-old to hit double figures in the new season.
"That's the objective for Jordan [to get more goals]," the Northern Irishman told reporters after the game. "The finish he produced to get the equaliser, he does that day in, day out in training.
"He's a player that is so fit and strong, and he's such a team player - he does a lot of unselfish work. This year we're asking him to get more into the box.
"I thought he had more opportunities when he played just around the corner [of the striker] in the last 20 minutes of the game - he was able to time his runs better going forward and he got in a few times.
"That's his strength - he can really penetrate the defensive line. I would expect him to be getting up to 10 goals this season because he has the quality and tactical awareness to arrive into the area to do that."