Bristol City travel to Nottingham on Saturday followed by a visit to West Brom after the international break.
"We have two very hard away games coming up and they will tell us where we are in this league," said Johnson, quoted in the Bristol Evening Post.
"I want us to try to be even higher in the table than we are and that means challenging the top two.
"That's where I want us to be."
Last season's corresponding fixture saw Forest come out on top in a five-goal thriller in which Dele Adebola, now a Red, looked to have secured all three points for City before late goals from Garner and Blackstock sealed a vital three points.