Royals boss Ruben Selles wants to snap up the goalkeeper from West Brom, but Button is waiting for a payoff to leave the Hawthorns.
Joining League One side Reading would see Button take a significant pay cut and he wants West Brom to help ease the financial pain.
While Button is tipped to be Reading bound, the Royals could yet have Championship competition for his signature.
Freshly relegated Southampton, Selles’ former club, are also keeping a close watch on Button’s situation in the Midlands.
Russell Martin is assessing Button as a possible backup goalkeeper on the south coast.
Reading are currently under a transfer embargo following a failure to pay HMRC on time and will need to resolve that situation to bring in Button.
Button, 34, came through the youth system at Tottenham Hotspur and completed a move to West Brom in 2020.
The shot-stopper has played at every level in the EFL.
