Hooper reports that Wests have "seen the light" and are looking to ramp up their interest in the Origin forward, who is yet to confirm his future past this season.
The Tigers have been keen on adding experience and leadership to their squad as they continue to seek a path back to the top eight, with Finucane a perfect candidate for the struggling Sydney club.
Finucane, a New South Wales product, has been heavily linked to a return back to his home state, with the Tigers joined by the likes of the Bulldogs, Dragons and Sharks in being reported as keen suitors in the past.
The Tigers will welcome international recruits Jackson Hastings and Oliver Gildart from the Super League at season's end, while Warriors flyer Ken Maumalo joined Wests last week following an immediate release.
The club are also understood to be weighing up a move for out-of-favour Broncos second-rower, who has been notified to assess his options elsewhere.