A win for the Scots could see them finish as high as third in Group A, while Croatia have already secured themselves a playoff spot behind leaders Belgium.
"We're looking forward to it," Sky Sports News quotes Brown as saying. "We have had some good results recently and we want to continue it.
"The week's training has been intense and we are enjoying it and we have got our shape sorted for the game. They have still got a lot to prove. They will come here trying to get the win."
Scotland earned a 1-0 win when the sides met in the reverse fixture back in June.