"I saw the surgeon last week on a follow-up check from when I had the op and he was really happy," said Simpson-Daniel.
"I've had no reaction so I'm training a little bit more aggressively now and fingers crossed for mid-August."
Simpson-Daniel missed England's summer tour to New Zealand as a result of the operation but hopes to return to club duty on either August 22 or 30 when Gloucester face Cardiff Blues and Glasgow respectively.
"There's no immediate hurry because it's not like we're mid-season and I need to try and get back for a big game or anything.
"Hopefully I'll start hitting some shields or whatever in the next few weeks. We'll see what my physio says.
"We've still got plenty of time until the first game of the season, but I'm ahead of schedule."