The Baggies are reshaping their squad under Carlos Corberan this summer and Button is not in his plans for next season.
Reading are keen on signing the 34-year-old goalkeeper, but Southampton have also been keeping a close eye on him.
Russell Martin wants to add an experienced backup goalkeeper to his squad and identified West Brom’s star as a candidate for the job.
Button has one year left on his West Brom contract and the Baggies gave him permission to talk to the Royals.
Now it has been claimed that Reading have managed to beat off competition to convince Button to join them.
However, his move will depend on the Royals transfer ban, which has been placed on them following failure to pay HMRC on time.
Now it remains to be seen whether Reading will be able to solve their transfer restriction issue to sign Burton.
