Great question — there's a lot of smoke, but nothing concrete yet. Here's the full picture from the wiki:
The trade rumors are real. NFL insider Jason La Canfora reported (citing an unnamed GM) that McCarthy may want out of Minnesota due to personality clashes with Kyler Murray since his signing. (from the J.J. McCarthy page)
Even more telling: NFL Network's Tom Pelissero said on June 4 that if Kyler wins the starting job — which oddsmakers peg at ~90% implied probability — trading McCarthy now while he has two years left on his rookie deal could be the smart move for Minnesota, because his value only decreases from here. (from the J.J. McCarthy page)
On the other hand, McCarthy publicly pushed back hard at mandatory minicamp on June 9, saying:
"I love this organization. I love the coaching staff. I absolutely love these players to death. This is where I want to be."
And HC Kevin O'Connell has described the QB room as "very professional" and "positive." So the organization is trying to project unity.
Bottom line: A trade is possible — especially if Murray clearly wins the job in training camp (decision expected in the first 1–2 weeks of camp). But it hasn't happened yet, and McCarthy is currently saying all the right things. Keep an eye on camp; if he's clearly the #2 and a team with a QB need comes calling, that's when the deal could happen.
On Fantasy Football Today, they summed up the vibe: most expect Murray to be the starter, and one analyst said he's "way better than what we've seen out of J.J. McCarthy" — .