The 31-year old is more concerned with Aberdeen.
Celtic's Scott Brown
The Gers have returned to the top flight after a four-year absence and are expected to challenge their bitter rivals right away, but Brown is more worried about last season’s runners-up.
Celtic's Scott Brown shoots
"I think Aberdeen (will be our main challengers) after the last couple of seasons,” said the Hoops captain.
"They are really exciting to watch and they came to Celtic Park last season and took points and we struggled up there so we'll need to do a bit better this season."
Mark Warburton is sure to use these comments as further motivation for his squad ahead of their league opener against Hamilton on Saturday.
Rangers manager Mark Warburton
The Ibrox club have made some shrewd signings this summer and, on paper, have a squad that is amongst the most impressive in the SPL.
It’s unclear how quickly the nine new signings will gel however, and how the rest of the squad will cope with the step up in quality of opposition.
Celtic manager Brendan Rodgers
Celtic will be confident of claiming their sixth title in a row but the return of Rangers has added new intrigue to a division that desperately needed it.
Brendan Rodgers has so far added just Moussa Dembele and Kolo Toure to his squad and he will hope to bring in more in the next month to ensure the Hoops can compete on all fronts.