Byrne, 30, has no intention of doing that just yet, but Laws saw something in his time working with the defender at Glanford Park that makes him thin the Irishman would make a successful manager.
Laws was back at the club on Sunday to manage the invitational side that took on the 2009 League One play-off winning team in Byrne's benefit match.
And while some of the names on show were rolling back the years having not pulled on a pair of football boots for a while, Laws insisted Byrne - who will be in Oldham's squad for a friendly against Manchester City on Tuesday night -was someone he would love to work with again.
"I wouldn’t hesitate to sign Cliff again, he has a tremendous attitude to the game, even when he’s finished playing I’m sure he will be in coaching or management, and it really wouldn’t surprise me," he said.
"It was a tremendous day for Cliff. He’ll look back over his nine years at the football club and will have a lot of fantastic memories. He has taken the club to heart, has settled in the area with a young family and he’ll be sadly missed around the place. But sometimes you have to move on in your career and I’m sure he’ll have the same impact at Oldham.
"The game itself tells you what his former teammates think of him and it’s fitting to see that nearly 3,000 Scunthorpe supporters turned out to say goodbye to Clifford.
"I have so many memories of Cliff’s time at Glanford Park, he was brilliant off the pitch as much as he was on it. One thing that stands out is his professionalism, not just in the game itself but he was a great role model for all players arriving at the club and was someone they could look up to."
Sunday's game saw a host of fans favourites return to don the claret and blue – or green – once more. The stadium had the feel of a school reunion, as teammates gathered together to relive great moments of the club's recent past.
Alex Calvo-Garcia, hero of the 1999 Division Three play-off final, was mobbed whenever he set foot outside the stadium
It is now eight years since he hung up his boots, but he relished the opportunity to return and play on the Glanford Park turf once more.
"As soon as Cliff called me I agreed to come back and share this important day with him. It is a great opportunity to come back and see all the players again, and really I wouldn’t miss it for the world," he said.
"Any chance I get to come back is fantastic, I had a wonderful time at Scunthorpe and people like Cliff are one of the reasons why.
I played with Cliff as I finished my career at Scunny and he managed to stay here for nine years which is an amazing achievement as you don’t see loyalty like that often.
"He really epitomises everything that this club represents. It is a small, family club but people are still able to move it forward. Cliff has shown fantastic loyalty to stay with the club so long and through all its recent success which demonstrates what a great player he really is. I’m sure wherever his career takes him over the next few years he’ll be just as successful as his passion, commitment and desire will ensure that it does."
The chant of "Cleeeeeeeveland" rang out from the terrace - and over the sound system thanks to match commentator Lee Turnbull - in tribute to Cleveland Taylor during Sunday's match.
The winger, who now plays for Burton Albion alongside former Iron Nathan Stanton, scored the opening goal. He felt Byrne was one of the reasons he settled so quickly in North Lincolnshire.
"Clifford is a top man and I can’t speak highly enough of him. When I first arrived at the football club as a young lad Cliff was one of the first players who took me under his wing and I actually stayed with him for a while," he said.
"As soon as he called me asking for me to play today there was no hesitation in my mind as I was always going to be here, no matter what.
"He’s been here through the club’s most successful period of all time, to think it took 50 years to reach the second tier of English football and Scunny managed it twice with Byrne in the side. Three promotions, one championship, one through the play-offs and one League Two runners-up as well as spending three out of five years in the Championship is some achievement."