Brown was particularly closely linked to a DJR switch at the mid-way point of the year.
Any lingering doubt over that was put to rest last Saturday when Erebus announced new two-year deals for both Brown and Kostecki, locking the pair in at the Holden/GM squad until the end of 2024.
An announcement on Davison's future with DJR could come as soon as the lead-up to the Sandown SuperSprint later this month.
When quizzed on the Erebus news, and what it means for his job security, Davison told Motorsport.com: "I haven't been stressed at all, all year.
"There's been a lot of talk, but we've just been focussed on our jobs.
"We all get along well, we're getting good results. There's been lots of talk, but I've been getting on with my business.
"I'm in touch with the people that know and the people that count, and we'll leave it at that for the moment. There's not much more to say.
"We're pretty easy going, we keep all that stuff to ourselves."
Davison has been in impressive form this year, currently leading teammate Anton De Pasquale in their qualifying head-to-head 12 to 11.
Both drivers have a win each and sit third and fourth in the standings, De Pasquale with the narrow edge on overall points.