Broadrick broke the news earlier today (27 April); Kozelek is yet to respond.
As Pitchfork point out, the two men have been linked many times in the past for various reasons. Kozelek's covered "Like Rats" - by Godflesh, another of Broadrick's acts - and referenced him in recent(ish) track "The Possum", released Jesu's 2009 LP Opiate Sun on his Caldo Verde label, and more.
Kozelek has his own LP coming out soon, Universal Themes, which is out in June on Caldo Verde.
There's no word yet on when the Sun Kil Moon x Jesu album might be arriving.