There are not too many rumors around what may be shown at E3, although even if there were, it would still just be rumors.
Regarding what facts we know about in regards to anything new coming for the PSVR, Shawn Layden, CEO of Sony Interactive Entertainment America had this to say:
"When a new console or new platform launches, there’s a lot of activity driving launch day," ... "And then there’s the inevitable lull between that and the next launch of titles. I think we’re seeing that happening now. Farpoint is the lead of that, and we’ll be talking about a number of other titles at E3."
From this, we can expect to see at least a few PSVR demos. E3 Media Showcase is set for 6 p.m. PT on Monday, June 12.