"He has been offered a job in America and there is every chance that he might want to go," manager Harry Redknapp told reporters after the Londoners' 1-1 draw at home to West Bromwich Albion in the third round of the FA Cup on Saturday.
"He wants to be a manager and it's a chance for him to go and manage a club," added Redknapp.
New Zealand captain Nelsen, 35, joined QPR from Tottenham Hotspur on a one-year contract in June. He played for DC United in Major League Soccer between 2001 and 2005.
"He's just one of the best pros I've ever met in my life," said Redknapp of a player he signed for Tottenham from Blackburn Rovers. "Fantastic player, great trainer, leader.
"He's a massive part of your team. To lose him would be a massive blow for us."
Rangers are bottom of the Premier League, level with Reading on 13 points from 21 games.