Millwall executive Andy Ambler was quoted in one English outlet stating that the club would be interested in acquiring Cahill on loan during the MLS offseason.
"We'd love to talk to Tim about that," he said. "If he turned around and said 'thanks but no thanks' we'd have to respect that but we would be mad not to ask the question. Every club would want someone of his quality at their club - but never say never. We would love it to happen. We would love to talk to Tim and his representatives but we recognise there will be huge interest in him.'
No comment from the New York Red Bulls when contacted by MLSsoccer.com about the report.
Cahill began a long career in England with Millwall in 1998 and played six years for the London-based Lions. The 34-year-old, who played a starring role for Australia at the 2014 World Cup, has just one goal and one assist this year after scoring 11 for the MLS club last campaign.
"I would sign Tim Cahill all day long, but I don't want to lift our fans' hopes only for them to be let down," Millwall manager Ian Holloway was quoted as saying. "I wouldn't want to put Tim in an awkward position where he would have to turn down Millwall - that wouldn't be fair. We all know he loves the club and that he's a fantastic player. If I had a chance to speak with Tim, I'd tell him that we'd love to have him back."