The out-of-contract Giant has been linked to a move out of Sydney in recent months, tipped to return home to Victoria in 2023, with both the Tigers and Collingwood reportedly keeping a keen eye on Taranto.
Speaking on Triple M, Browne revealed that the Pies have cooled on their pursuit of Taranto, instead casting their eyes towards another Giant in Bobby Hill.
"I think Taranto is now leaning towards Richmond."
The uncontracted Taranto has played 16 games for the Giants this season, averaging 25.4 disposals, 3.8 clearances and 4.8 tackles per game.
He has played 114 games for GWS in total since his debut in Round 1, 2017.
Fellow Giant Hill requested a trade at the conclusion of the 2021 season to Essendon, but a deal was never reached between the parties. After being drafted in 2018, the small forward has played 41 games across his career, playing only 11 in 2022 after being diagnosed with testicular cancer in May.
The 22-year-old made an inspirational return to the VFL last weekend, playing in the Giants' last game of the season.
The AFL's trade period is set to begin on Monday, October 3.