Targett has been a big hit on Teesside since joining the Championship club on a season-long loan in the summer, playing a key role under first Rob Edwards and now Kim Hellberg.
His contract at Newcastle expires in the summer and the 30-year-old says he "believes he's done" at St James' Park.
The dream scenario now for Targett is helping Middlesbrough win promotion and then signing a permanent deal at the Riverside in the summer.
But if Boro opt against making his deal permanent, Targett believes he's shown this season that he still has an awful lot to offer and that hopefully his injuries worries are behind him.
Targett was a big hit on Tyneside when he first joined Newcastle on loan in the January of 2022 and he made the switch permanent for £15m.
But Targett's time with Newcastle was heavily disrupted by injuries and he made just five Premier League appearances in his last two full seasons on Tyneside before linking up with Boro.
It's been a different story this season, however, with Targett quickly establishing himself as a regular for Boro and making 35 Championship starts.
RECOMMENDED READING:
It briefly looked as though his loan spell on Teesside might be cut short in January when Newcastle were facing an injury crisis, but Targett was grateful to United boss Eddie Howe for letting him see out his time at Boro.
Targett said: "There was a lot of talk about that. A lot of defenders picked up injuries at Newcastle and there was some stuff floating about,
"I actually had a chat with Eddie and he was so understanding of me and my position. For him to let me stay here and carry on playing football and enjoying my football here was very important. I can't thank him enough."
Targett wanted to stay at Boro because he's loved his time at the Riverside but also because he knows he's playing for his future.
Asked what he expects to happen this summer, the left-back told Sky Sports "I'm not sure yet. I believe I'm done ay Newcastle. That chapter is closed.
"We'll see. Hopefully I get promoted here and there'll be a contract, but if not I've played as much as I can and I'll assess my options.
"It was very important I came and played. Whether it's left wing back, left back, with the injuries we had at centre-back. I've enjoyed playing and that's the most important thing. especially at the age I'm at now."
Looking back on his time at St James' Park, Targett said: "It was so frustrating my time up at Newcastle.
"When I went on loan I loved it and played all the time. I picked up a few injuries and it was hard to get back in the team and the team progressed so quickly.
"They have some unbelievable players up there now and they're only going to get better and better.
"I had two and a half, three years not playing much minutes. It was really important for me to come here and get minutes to prove to everyone I can play a full season without injuries. Thankfully I've done that, I'm in my last year so it was very important I came and played."