The right-back's current deal is due to expire this summer and despite the fact that he has made 19 appearances in the Premier League so far this campaign, it has been decided that he will not be offered an extension by the club.
"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."
The 26-year-old originally joined the Magpies from Manchester United on a loan basis in 2009, before signing a permanent contract a year later.