Nope - and, so far as I'm aware, no site that even just lists who's injured, let alone any comments on what the injury is, or the Expected Return to Action.
Different clubs have different protocols on this, and given patient confidentiality; would need permission from the individual players to say anything at all anyway.
Some clubs will list this week's "Unavailable for Selection" with the team announcement each week, some will update their local rag, or their offy website on a semi-regular basis; some will cover it under "Playing Squad 2016-17" on their offy website, and some will say nothing at all, ever. Obviously, when players turn out for interviews or analysis for the local radio coverage, they may talk about injuries then as well, but would have to be very careful talking about anyone but themselves for injury status.
I used to try to host a page on a couple of sites, updating injury statuses for all Prem clubs; but it was an absolute fool's errand; then for 4-5 years my club (Bath) stopped releasing anything at all, and I had to go by my own opinion of what I'd seen on camera and the occassional but of gossip from interviews etc; and even just keeping up with 1 club was a fool's errand. I quit even trying about 4 years ago now.