He told BBC Radio Lancashire: "It's going really well. I'm ahead of schedule. I was concerned that I'd done something worse than I actually did."
"They operated on it. It went really well, I'm ahead of schedule and I just can't wait to get back out there."
The England under-21 international was injured in the 1-1 draw against West Ham, the first match in charge for Rovers manager Steve Kean.
Jones said: "Hopefully I'll be back out (on the training pitch) next week doing the warm-up and maybe a bit of training.
"And, then the week after that I hope to be back out there training properly."
Jones recently signed a one-year contract extension meaning he is now tied to Blackburn until the summer of 2016.
Source: BBC Sport