I'd imagine Couturier would be plenty available. In a vacuum, he'd probably even be a great "stopgap" for the Habs. However...3 more years @ $7.75M on a guy who is clearly slowing down (and wasn't fast to begin with) and has noted back issues, is definitely suboptimal. Probably a non-starter.
The idea of retention is probably out of the question...especially considering the Flyers have absolutely no pressing need to move him whatsoever. In fact, it's very likely they'd prefer to just hang onto him unless someone blows their socks off. They need playable NHL Centers with experience and some two-way ability who can hold up defensively but also have the skill and smarts to play with talented younger players as well, as they try to bring in young players as they rebuild. As long as he's willing to keep plugging away at it...he seems like a good solid veteran leader to keep around along with Konecny, to help insulate and mentor the kids as they come along...avoid falling into that Buffalo pit of despair scenario.
The only way to really balance that would be something like Josh Anderson going the other way to offset a big chunk of it. But the Flyers need another RH Winger like a hole in the head. So...that's also probably a non-starter.
I think Couts injuries, decline, and contract make him pretty close to unmovable...even in a league that is absolutely starved for even a 2/3C "tweener" with size and some defensive conscience.