The 35-year-old has been one of the west Londoners' few shining lights this season, having joined in June following spells at Blackburn and Tottenham. Nelsen has made 21 appearances in all competitions but now looks set to leave Loftus Road to take up his first managerial role.
Press Association Sport understands the defender is in Toronto to discuss the vacant post, having been granted a few days off training by manager Harry Redknapp. It is unclear whether the job in Canada would also see him make a playing a return to MLS, having made his name there during a four-year spell with DC United.
The Washington club were another linked with a move for Nelsen, who has reportedly been swayed to Toronto by their president and general manager Kevin Payne - an executive at DC United when he played there.
Nelsen's departure would be a huge blow for QPR, who have won only two of their 21 Premier League games this season. Redknapp signed Nelsen when Spurs manager and has regularly highlighted his significant role at Loftus Road.
"Nelsen is very important to us, a fantastic leader, a top player," the Rs boss said after the 1-1 FA Cup third-round draw with West Brom. "He has been offered a job in America and I think there is every chance he might want to go.
"He wants to be a manager and it is a chance for him to manage a club. He has been fantastic. I took him to Tottenham last year from Blackburn. He's one of the best pros I've ever met in my life, a fantastic player, a great trainer. He is a massive part of your team. To lose him would be a massive blow for us."
Meanwhile, QPR have released Kieron Dyer just days after the midfielder scored his first goal for the club.
The 34-year-old former England international joined Rangers in July 2011 following his release by West Ham. Dyer, whose career has been beset by injury, made just eight appearances in all competitions for QPR, who have opted to activate the release clause in his contract despite his goal in Saturday's 1-1 draw with West Brom in the FA Cup.
"I'd like to thank Kieron for his services to QPR," Redknapp told the club's official website, qpr.co.uk. "If he can stay clear of injuries I'm sure there's clubs out there that will offer him the chance to play football. He wasn't in my plans and I think he's got something to offer someone, so we wish him all the best."
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