According to a report from Dan Walsh on NRL.com, the Cowboys are keen on signing the Storm lock.
However, there are other clubs circling for Finucane, who has played four games for the Blues and was in the extended squad for Game 2 of this year's series.
He may well have been selected for Game 1, had he not spent the first part of the season injured.
The Storm have expressed their desire to hang onto the representative forward, who has turned into one of the game's best since his move from the Bulldogs.
Under the coaching of Craig Bellamy, Finucane has gone from bench forward to Origin-level lock, and it's little wonder other clubs would like him in their colours from 2022. It's reported both the Wests Tigers and Newcastle Knights are weighing up their options.
The 29-year-old, who has cleared 200 NRL games and is co-captain of the Storm, has done an excellent job in helping lead his team in the absence of retired former captain Cameron Smith.
The Storm sit equal top of the table after 15 rounds, and with Finucane averaging 120 metres per game, while also tackling at 96%, it's not hard to see why he has had a major hand in their climb.
Taumalolo signed a long-term, ten-year deal with the Cowboys which will see him with the club until the end of 2027, but his form has tailed off under new coach Todd Payten.
Finucane is thought to want to end his career in the Melbourne system, however, with salary cap constraints squeezing the club, the lock may have a decision to make in the coming weeks.