Leichhardt Oval's $40 million renovation is expected to keep the Wests Tigers away until 2028.
Campbelltown Stadium is expected to host six home games, while CommBank Stadium is tipped to stage about four.
A Magic Round home fixture at Suncorp Stadium is expected to be the club's last there.
The Tigers begin their campaign in Las Vegas against Melbourne Storm.
The Sydney Morning Herald reports Dunedin's Forsyth Barr Stadium is the leading option for a Tigers home game.
The club was first approached about playing in Christchurch, Hamilton and Wellington.
The move could promote league in the South Island, where the Southern Orcas are pursuing the NRL's 20th franchise ahead of the Ipswich Jets.
Coach Benji Marshall's New Zealand connection is also understood to be a factor in the discussions.
The Sydney Morning Herald also reports two Sydney powerhouse clubs are discussing a pre-season trial at the venue.
A fixture during the week of State of Origin II in Auckland was also considered.
The 2027 draw is due to be released on November 12, with the Tigers' home arrangements a major issue.