The 34-year-old goalkeeper joined the Baggies from Premier League side Brighton in the summer of 2020.
Button started last season as the first-choice goalkeeper for West Brom, but after the arrival of Carlos Corberan, he found himself down the pecking order.
The West Brom boss omitted Button from his 22-man squad in their last two pre-season games against Salford City and Cheltenham Town.
Reading, who were relegated last season, are showing interest in the veteran goalkeeper in the ongoing window.
Now it has been claimed that Button has received permission from the Baggies to discuss a potential move with Reading.
The Royals are reshaping their squad to get back in the Championship and believe that Button can play an important role for them.
Button has one year left on his contract with West Brom and it remains to be seen whether Reading will be able to agree a deal with the goalkeeper.
