The qualifying offer has to be made within 5 days after the world series concludes and players have until Mid-November to accept (roughly 10 days after the QO is made). The current CBA doesn't expire until December 1st, so the QO still applies to this crop of free agents. Whether or not the QO is a part of the next CBA doesn't apply.
The QO is a no brainer. That is the only way it makes sense to keep Jeffers. However, Gleeman has insinuated that the Twins are viewing the QO more like a 50/50 chance. Yes, Jeffers was at peak value near the trade deadline, but he had also missed 8 weeks due to the hamate injury. We don't know what was offered for Jeffers, but several outlets confirmed there was interest in Jeffers. However, the value you would have received from a 2 month rental that just spent 8 weeks on the IL probably would have disappointed most. In that case, the value of the comp pick we would get if Jeffers turns down the QO is probably similar to the return we would have received.
The question is, will Jeffers take the guaranteed 1 year payday of the QO given the uncertainty of the next CBA? Who knows, but worst case scenario is we have Jeffers on a 1 year short term committment. He will have to make that decision prior to the current CBA expiring.