Round worked with McClaren at Middlesbrough and in the England set-up and spent the second half of the season on the coaching staff at Derby.
But the long-term No 2, who was Sam Allardyce’s assistant at Newcastle and David Moyes’ right-hand man at Everton and Manchester United, has rejected McClaren’s latest job offer to pursue a first manager’s job of his career.
He told Sky Sports News HQ: “We spoke a couple of days ago, and he asked if I’d be interested, but he also knows it’s not what I want to do next. I want to be a head coach or a manager.
“That’s no disrespect to Newcastle. I worked there for a year with Big Sam and Kevin Keegan, and it’s a magnificent club with great supporters, but at the moment I don’t think I’ll be joining them.
“To be a head coach or manager is my No 1 target. If that doesn’t happen in the coming months I’ll have to drop back to being a No 2 or coach, and I’ve got no problems with that.”
Newcastle took the unusual step of appointing McClaren to the board when he was named boss, and Round reckons that position will help when it comes to introducing a “coaching philosophy” on Tyneside.
He said: “Steve’s got a tough job. After last season he’s got to rebuild the club, so it’s a tough job, but it’s also a great job. And with him sitting on the board he should be able to implement the changes he needs to implement.”