You have to think of him as a player looking to cash in as a free agent in July 2019. Leave all talk of extensions on the wishful thinking pile. That means you get two playoff years with Karlsson if you acquire him.
As has been stated, this would figure to be a really tough trade to work out. The Sens will want full value for him as a player. That's a very high-end player. However, acquiring teams would have to look at him as a rental + one season. That has more value than he would have as a pure rental, but still nowhere near where the Sens would value him. So the likelihood that offers are perceived as insulting is high right now.
For this reason, I don't think anything would get done until the Senators' perceived value of him as an asset shifts, and I don't think that happens until at least the summer, possibly not until next season's Feb/Mar 2019 deadline.
As time passes, his value as an asset will depreciate. If they're not going to table a competitive offer, they should know that already, come to terms with it, and trade him while an acquiring team gets two playoff years with him. Wait, and the team trading for him is only assured of getting one playoff year with him, and that makes him a rental. Adjust prices accordingly.
Borking his feelings about Ottawa is the fact that the cap is about to steeply rise and Ottawa already won't spend to the cap now. What happens as teams start overspending Ottawa even more? More than anything else, the feeling that Ottawa isn't a cap team while revenues are spiking is affecting his decision making today. They should know that he's probably not sticking around.
Only teams with a plethora of assets need apply, I imagine. I like the possibilities from a team like Nashville. They check all the right boxes in that they are a contender, thus willing to deal some futures, with lots of assets on hand (both young and mature) in order to make a deal. I still doubt that any team would offer enough right now, though.