The Guardian reports that world number four Patrick Cantlay and world number six Xander Schauffele are among four new players being courted by the breakaway tour ahead of the start of its expanded 14-tournament second season.
The inaugural LIV Golf season wrapped up over the weekend with Dustin Johnson's four aces GC winning $16m prize money in the Team Championship.
Asked about the reports linking Cantlay and Schauffele with LIV Golf, the organisation's president Atul Khosla refused to be drawn on specific names, but did say they were in the process of finalising a new wave of signings.
"We are in the middle of the discussions. We are going to get it done this year. We want the teams locked in by the New Year. It will play itself out over the next couple of months," he said.
Other players being linked with a move to LIV include European duo Mito Pereira and Thomas Pieters.
Pereira very nearly secured his maiden major win at this year's PGA Championship before ultimately finishing third, while Pieters is one of Europe's top performers and a strong Ryder Cup candidate.
Signing Cantlay and Schauffele would be a major blow for the PGA Tour in its ongoing battle with the Saudi-backed breakaway tour, however, and they've already taken several hits with the losses of Dustin Johnson, Bryson DeChambeau, Brooks Koepka and Cameron Smith.
So far, Cantlay, Schauffele, Pieters and Pereira have not offered any comment on the rumours, either on their own social media channels or via their representatives.
Meanwhile, LIV Golf's new schedule is expected to be released by the end of November, while it is also in talks to secure a television broadcasting deal, with current figures very low due to LIV Golf events only being broadcast on YouTube and the LIV Golf website.
"On the US front, we are back and forth with a few different networks," said Khosla.
"I feel good about where we are but we have work to do over the next couple of months. We think we are providing an incredible commercial product. These are not six-month or one-year deals, if a TV network is getting behind this it's for multiple years. We have got to start commercialising the product. We have got to get on TV, we have to get corporate partners. These are milestones that we need to hit."