Bertuzzi is one of those players who you are content to have but open to trade if the right offer comes on the table. He brings good value to the roster, can go up and down the lineup.
If one look away from the vaccine thing. Personally I think the Red Wings should explore the options of trading him. He is 27 now and even though would be nice to have on a contending team in the future, I'm not sure he would provide the same value then in regards to what Detroit should use on him (needless to say he could provide it).
As for trade partners, I think the Los Angeles Kings or New York Rangers would make sense both in terms of their current roster builds, what they might be looking to add, the size and term of Bertuzzi's contract and what they can offer in a package to Detroit that would make sense.
The Rangers need to re-sign Strome, Kakko, Blais and add a backup goalie. Which I think they can maneuver their way into doing that even if adding Bertuzzi, and his contract is up after next season, along with several other players they have, so it gives them options to decide what they will do going forward.
In addition they have several cap buyouts ending at that time and their main guys are into a win now/very soon mode. They wanted to become a bit more grittier, they could use more scoring into the top 9, age wise and playing style a match with the roster build, Bertuzzi just fits the mix.
The Kings with some of their guys currently on IR can make Bertuzzi fit for this season cap wise. They have some cap coming off retained after this season and little bit after next season.
With Dustin Brown, Athanasiou, Kempe, Lemieux, Lizotte, Grundstrom, Maatta, Edler and others coming off the books in the offseason they have a lot of freedom to adjust however they like, and with Bertuzzi only on contract until next season, they don't lock themselves into any specifically difficult positions when it comes to re-signing players or upgrades.
For a team with a win now mode, even though not the absolute strongest on paper, adding Bertuzzi with his cap, term and playing style could be a good fit within their needs in the lineup. I could see them potentially making such move and add a depth Chara if it fits the books.
Return wise both have assets to come to an agreement. The Kings with a better fit of prospects they could offer in regards to Red Wings needs.