Donald Trump might think that Michael Flynn’s testimony for probes into Russian influence in the previous election cycle justifies an immunity grant, but that’s not the opinion on the other end of Pennsylvania Avenue. According to CNBC, the Senate Intelligence Committee has rejected the former national-security advisor’s request — at least for the moment:

The Senate Intelligence Committee has rejected Michael Flynn’s request for immunity from prosecution in exchange for his testimony in the panel’s probe into alleged Russian meddling in the 2016 election, congressional sources told NBC News.

The former national security advisor’s lawyer was told immunity was “wildly preliminary” and “not on the table” at this point, a senior congressional official told NBC. It does not necessarily rule out immunity at a later date, as the Senate investigation is ongoing.

At NBC, the report adds a second source:

A senior congressional official with direct knowledge said Flynn’s lawyer was told it was “wildly preliminary” and that immunity was “not on the table” at the moment. A second source said the committee communicated that it is “not receptive” to Flynn’s request “at this time.”

“Wildly preliminary” can mean a couple of different things. One big point is whether the committee is even prepared to deal with Flynn’s testimony yet. At first blush, it appears that they have only just opened communications with Flynn and/or his legal team. If that’s the case, then Flynn will not have yet allocuted privately about what his testimony will include, which means the committee can’t judge whether it’s worth immunizing him. The report does leave the option of immunity open in the theoretical sense, which is the same status as Flynn’s testimony for now.

Even with that theoretical possibility still open, Flynn’s request — and Trump’s endorsement — didn’t sit well with the House Oversight Committee chair, either. Jason Chaffetz told Fox News that Flynn shouldn’t get immunity at all from Congress while the FBI is still investigating the matter, and that it wasn’t appropriate for the president to comment publicly on the request under those circumstances:

Jason Chaffetz: Flynn shouldn't be given immunity & @POTUS shouldn't weigh in https://t.co/ydD12zcyCU pic.twitter.com/R2UcLt42bs

— Fox News (@FoxNews) March 31, 2017

Rep. Jason Chaffetz (R-UT) said this morning that Congress should not grant immunity from prosecution to Gen. Michael Flynn amid the ongoing FBI investigation into Russian meddling in the 2016 election.  …

Speaking with Bill Hemmer, Chaffetz said he does not believe there is a “witch hunt” going on, referring to the language used this morning by Trump on Twitter.

“It’s mysterious to me why all of a sudden General Flynn is out there saying he wants immunity. I don’t think Congress should give him immunity if there’s an open investigation by the FBI,” said Chaffetz.

In other words, Flynn had better have a pretty good reason to demand immunity, and he’d better wait until Congress wants to cross the FBI stream to probe the issue. Until then, all of this discussion is, er … wildly preliminary.