The right-back is out of contract in the summer, and looks set to depart Newcastle after four years at the club.
Simpson has made just 19 appearances in the Premier League this season for Newcastle after suffering injuries to both toe and hamstring.
With the club signing Massadio Haidara and Mathieu Debuchy in the January transfer window, Simpson will not be offered a new deal in the North-East.
Asked if he expected to leave Newcastle this summer, Simpson admitted that he would probably be on his way through the exit door.
"I think it does look that way, unfortunately," Simpson told TalkSport.
"We've had chats and there are no bad feelings. I've given everything while I've been here at the club. It's just one of those things in football.
"I'll definitely miss the club. I've been here for a big part of my football career. I've been here for four years and I've enjoyed every minute of it."