Let's do the exercise pretending there is an actual plan to re-sign Jeffers to a FA contract. First, you should have tried to do this last offseason if you are actually serious about trying to sign him to an extension. Below is the list of the current highest paid catchers with their current contracts. If you don't see a contract, it means they are still under arbitration. Jeffers isn't worth the top 3, and a new contract is likely in the range between the lines (Salvy and William Conteras). The current QO is $22.025 million. For the people who want the QO, you're asking the Twins to pay nearly $5 million OVER the highest paid catcher in MLB. Doing a QO makes no sense for a catcher. This seems absurd for a catcher all for the privilege to get a draft pick in either at the end of the 1st round or the end of the 2nd in which you will have to wait 2-5 years to see any results for. Our drafting and developing hasn't had the best track record in the last decade or so. Also, if you thought that we had no bullpen help now, take away another $5 million and see how our bullpen will be next year.
My theory would be to try to entice him with a 3/$42M or a 4/$50. You are overpaying in AAV for fewer years as an honest contract would be near Murphy and Kirk. I still think that if you were serious about bringing him back, you would have already tried to re-sign him.
All of this to say that they should probably trade him for the best offer they can find provided they are not giving him away.