Dyer will sign a pay-as-you-play deal with Middlesbrough in the next 48 hours.
Tony Mowbray held one-on-one talks with Dyer, who was released from his previous contract with QPR at the start of the transfer window, last week.
The 34-year-old has made 47 appearances in the last five-and-a-half seasons, due to hamstring problems and a broken leg in 2007 that effectively wrecked his career at West Ham United before it had really started.
Tony Mowbray: “Nothing is finalised yet, there's no pen put to paper, but it could be exciting for us.
“He's not in his middle 20s like he was at Newcastle, but watching the footage of him from this season and seeing the way he was chasing Gareth Bale and matching him, the Championship could be somewhere where he could flourish.
“I think Dyer playing in the Championship will be very different to Dyer playing for QPR in the Premier League.
"I haven't signed him to play at right-back, although there might be a scenario where we need him to do a job there for us, I see him playing further up the pitch, playing between the lines.
“From a very early age, Kieron knew when to run, when to stand still and knew which areas to put the ball in.
"He's been abroad after leaving QPR to clear his head and we just managed to pick something up last week. We'll see if we can conclude something in the early part of (this) week.
“If we can get him on the field, he'll be a big asset.
“If we don't get him on the field, then he isn't going to cost us much money at all. It'll be a deal that suits both parties, but I've spoken to Kieron and he really just wants to come and play.
“Assuming he is fit and ready to play, we'll have to manage his working week and try to get him on the field on a Saturday. He's not going to be able to play three games a week, but we know that.
“I've always liked him. He was breaking in as a 17-year-old boy when I was a player in my late 30s and he was some footballer as a young man.
“He knows myself, he knows (assistant manager) Mark Venus and he knows Woody (Jonathan Woodgate) very well from his time at Newcastle. I think he'd like to come and help us.”
Source: Newcastle United Mad