The English right-back says he has enjoyed his time at St James' Park but looks set to leave the club upon the expiry of his contract following the signing of Mathieu Debuchy
Simpson, who joined the Tyneside club in 2010, has only made three starts since the turn of the year following the January signing of France international Mathieu Debuchy.
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Asked if he was likely to be leaving the Toon in the summer, Simpson told talkSPORT: "I think it does look that way, unfortunately.
"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."
Simpson has played 138 games for Newcastle and scored two goals.