Simpson targets late September return for Newcastle
The 25-year old right-back suffered a hamstring injury in the weekend's 1-1 draw with Aston Villa which will keep him out until late September following a recent scan.
"It's a lot better than I first thought," Simpson told the club's official website.
"I have never had a hamstring problem before. I just felt something bad and I knew straight away I would have to come off.
"But the scan results came back on Wednesday and it is hopefully three weeks, maybe four maximum.
"It depends on each person, their body and how quickly they recover, but it's a lot better than what we first thought.
"Already I'm walking easier than I was on Sunday, so that's a good sign."