I suspect that there is no market for Brannstrom outside of the Senators including a sweetener.
There would have been a market for him at the draft or earlier in the off-season. Although, the return would have been minimal. Nobody has cap space. Garrioch flubbed the script a bit when he talked about the Senators needing Brannstrom, but also waxed-poetic about how he might even clear waivers.
The way the Senators defense is built, they could go with 5 defenseman if needed and not miss a beat. That is why it is hard to believe that plugging in any of their tweeners to the #6 spot to play a few minutes a night at even-strength is an issue. They would miss Brannstrom on the PK, but they can make those minutes up by giving Chychrun more PK time. Chychrun basically is not being used on the PK right now, which is ideal, but I think he can handle going from 21 minutes a game to 23.
The primary issue with moving out Brannstrom is depth in regard to injuries, but that's always going to be an issue with the defense.
I think the issue is more that they don't want to lose another 2nd or 3rd round pick by having to attach one to Brannstrom to get someone to take him. I doubt there is a market for either Brannstrom or Kubalik without a sweetener. Nobody has cap. For the teams that do have both cap and real money to spend to back it up, giving up any of that cap comes with a massive opportunity cost. If a team gives up 2M or 2.5M now and take Brannstrom or Kubalik for future considerations, they lose out on multiple draft picks at the deadline where they could be a third party to facilitate transactions. Or, they lose out on a 2nd round pick to be a dumping ground for a bad contract like Chicago was last year for Zaitsev.