The 25-year-old damaged his hamstring in a 1-1 draw at the weekend but a scan has alleviated the club's initial fears and he could be back in three to four weeks
The 25-year-old pulled up during the 1-1 draw against Aston Villa and admitted to being worried regarding his lay off with the injury being the first of its kind to affect the right-back.
However, results of the scan have boosted the former Manchester United player's confidence and he has now targeted a three- to four-week lay-off.
|33/1||Newcastle are 33/1 with PaddyPower to beat Everton 3-1 after the international break
"It's a lot better than I first thought,” he 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.
The international break has come at a good time for Newcastle manager Alan Pardew, with a number of his defensive options currently carrying knocks.
Ryan Taylor has been ruled out for the foreseeable future with a cruciate ligament injury, will James Perch and captain Fabricio Coloccini are also carrying hamstring strains.
And Simpson sympathises with his manager and fellow crocked defenders, adding: "Injuries are part and parcel of being a footballer, but I'm not used to it - I haven't had many injuries.
"With there not being a game for two weeks, if there is a time to have a little niggle then it's probably now.
"I will just have to see how it is at the start of next week and take it from there, but hopefully I won't miss too many games.”