Trouba is out for a few weeks, and Kulikov is already out. Jets could be looking for a guy like Cole or Hunwick, although Cole seems more of a fit than Humwick does. They also have a bit of a jam at C once Schiefele gets back. Scheifele, Little, Lowry, and Wheeler though he usually plays wing. They have some others that can play C when needed, Perreault, Roslovic, Hendricks(Pass).
It would be nice to get Roslovic, problem is he is unproven in the NHL (only 8 or so GP), but he has been dominating the A this year (35 pts in 32GP in his second season, 48 in 65 last year). I don't think the Jets would move him, and I don't think JR would consider him due to him being green. Maybe Perreault could be had as a hockey trade, but he's in the middle of a career year so price could be inflated. He's also signed for 3 more seasons.
Wheeler, Hendricks, and Enstrom are UFA's at the end of the year, but the Jets have been good so I don't see them moving Wheeler or Enstrom and Hendricks shouldn't be on our radar.
Tl;DR I don't see a fit.