Mark Geragos, the attorney repping the Menendez brothers, joined us Tuesday on "TMZ Live" and told us he's filing documents today asking Gavin Newsom for clemency.

That's pretty significant on its own, and sources connected to the Governor's office tell us they have the clemency petition on their radar ... which is pretty interesting, considering Newsom talked about the Menendez brothers in a recent podcast.

Gov. Newsom weighed in on Erik and Lyle's situation on "Politickin' with Gavin Newsom, Marshawn Lynch, and Doug Hendrickson" ... saying he was told to keep an eye out for them because of the Netflix documentary, and praising Ryan Murphy for producing a compelling show.

Newsom says he's actually going over parole board recommendations, pardons and commutations not related to the Menendez brothers ... saying this time of year before the holidays is when a lot of that work gets done.

Geragos also confirmed what we first reported ... that Erik and Lyle's legal team is also planning to ask the judge in their resentencing hearing to change their conviction from murder to involuntary manslaughter, which would immediately set them free based on time already served.

There's also a new judge in the case and the upcoming resentencing hearing is on track for next month ... but it sounds like Geragos may be able to spring Erik and Lyle sooner rather than later.