Mohr broke the news on Twitter, stating simply, "About to do my voice over work for new Saints Row video game." Alongside this message Mohr posted a photograph of the recording studio he was using where a screen clearly shows several fan-favorite Saints Row characters.
Unfortunately, Mohr's image offers no further hints at what the actor's involvement might be in the Saints Row universe. Saints Row 4 is a new enough game that this recent recording session may be related to an upcoming, as yet unannounced DLC addition for the game. On the other hand, the game is also old enough that developer Volition could have pulled Mohr in to record lines for Saints Row 5. While not necessarily a direct indicator of his role, Mohr previously voiced Dane Vogel, antagonist of Saints Row 2.
Whatever the case, we likely won't know more any time soon. Mohr's become coy since his initial reveal, and neither Volition nor publisher Deep Silver will say anything further.
Edit: This article has been altered to note that Jay Mohr previously appeared as a voice actor in the Saints Row series.