Personally I don't think we will be able to find a suitor for Zaitsev before the deadline. He and or Connor Brown will be moved in the off season though, that is pretty much certain at this point. The point of this post is to try and find a realistic suitor for him with a realistic return and how that would look before the deadline.
I actually don't hate Zaitsev as much as most do, it's really just his contract that's the problem. He might not be the best puck mover, and needs to improve his gap control, but I think he's really good at separating guys from the puck in his own end, he's a good penalty killer and isn't too bad in the offensive zone at getting pucks through.
Realistically if his contract was something like 2.8 million x 3 or something along those lines, we would first of all want to keep him, and secondly be able to trade him for a 2nd or 3rd rounder. But considering his contract, which is unfortunately signing bonus heavy, he becomes way less attractive on the trade market. Strictly just talking picks, he's probably worth a 5th or 6th rounder, but that'd be a big risk for the team taking him on, most team would want a more guaranteed asset with him to sweeten the deal.
All this being said, I also don't think Zaitsev has reached his full potential on the north american pads and I'm sure there are some GMs that could be convinced of this too with the right deal. I mean if we were able to trade Dion Phaneuf and his horrible contract, anything is possible.
New York Rangers and Ottawa Senators are the teams that jump out to me as suitors. Both are team that are going to be around the cap floor for the next few years, have struggled defensively and on the penalty kill this year, and are rebuilding. If Zaitsev is packaged with the prospect it could make sense for both team. Toronto would also have to recoup a RD for this playoff run though as well.
Zaitsev could be the perfect stay at home D partner to put with Chabot, the new version of the Karlsson Methot pairing of the Sens' glory days.