Ephraim has fallen out of favour at QPR in recent seasons, taking in loan spells at Leeds, Charlton and Bristol City.
Payne hopes to complete a loan deal for the 24-year-old in the next 48 hours.
"We're in hopefully the final stages of signing him to a loan agreement with Queens Park Rangers," he was quoted as saying on the official MLS website.
"We hope that will be concluded in the next day or two."
Reports suggest attacking midfielder Bostock and striker Earnshaw will arrive at the Canadian club on Wednesday.
Earnshaw recently took in a loan spell at Israeli club Maccabi Tel Aviv and is out of contract at Cardiff in the summer.
Payne added: "[Earnshaw] arrives to take a look at us and for us to take a look at him to see if that's a fit that might work.
"It's a little too early to tell if that's going to happen."