The Celtic manager says his captain could improve in this area.
The 31-year-old midfielder has helped Celtic to five straight Scottish Premiership titles - and won six overall - and Rodgers will be hoping that Brown can help deliver him a top-flight crown in his first season at Paradise this year.
The Scotland international is hardly old, but there are plenty younger knocking around too and Brown might have been conscious that he might have to work harder to impress the new manager, who replaced Ronny Deila this summer.
And Rodgers says that indeed he has been very impressed by him thus far, but admits that his passing could be stronger.
"His passing is good and he can open it up at times. Of course, like any player it could be better," he said to Herald Scotland.
"But he can really drive the team, hunt and press. Then he has the calmness to make the first pass when he wins it. So he has really impressed me."
Brown will be relishing the upcoming season; not just because Celtic will be hoping for a sixth straight title, but because Rangers are back in the fold.
Midfielder Joey Barton has already thrown down the gauntlet to Brown by insisting he is a much better player in comments which add spice to what will already be very hostile Old Firm derbies this season.
Before that, though, Celtic must qualify for the group stages of the Champions League, and they can go within 180 minutes of doing that tonight if they see of Astana in Glasgow, with the tie finely poised at 1-1.
Celtic's Scott Brown celebrates with the trophy and team mates after the game