Nelsen left Loftus Road in January to take over as coach of Toronto and the club's president, Kevin Payne, has listed Ephraim as one of several players he is looking to sign ahead of the 2013 MLS season.
"We're in hopefully the final stages of signing him to a loan agreement with Queens Park Rangers," Payne told the league's official website.
"We hope that will be concluded in the next day or two."
Tottenham midfielder John Bostock and Cardiff forward Robert Earnshaw are also rumoured to be close to moving to the Canadian franchise with Payne confirming the deals are all likely to be temporary.
"All of these players would initially be on loan because we want to be able to have an opportunity to see them in our league before we make long-term commitments," he added.