The venture club's interest comes as the Cowboys continue their press to sign Tigers lock Luciano Leilua on an immediate release, with the 25-year-old already set to make the move to Townsville at the end of next year.
The Cowboys had reportedly placed hooker Reece Robson as a potential asset in their negotiations with the Tigers to fast-track Leilua's transition north, with Michael Maguire and Tim Sheens standing firm in retaining their gun forward until the end of his current contract.
The Tigers are now looking to the future to succeed Leilua from 2023, evening casting their attention to North Queensland's youthful back-rower stocks.
According to Fox Sports' James Hooper, the Tigers have tabled a two-year offer to Nanai worth $600,000 in a move to "hit back" at the Cowboys' advances.
Should Nanai agree to the Tigers' terms, Maguire and Sheens may then look to rekindle negotiations with North Queensland as part of a potential straight swap prior to the 2022 season.
Nanai is touted as one of the NRL's most exciting young forward talents, impressing in his four appearances for the Cowboys late into this season.
The New Zealand-born second-rower scored a try in his debut - which coincidentally came against the Tigers - and averaged 78 running metres per match.