The 32-year-old former Ireland international started 11 Premier League games for Steve Clarke's side last season and the two parties were in talks about extending his stay at the Hawthorns.
However, an agreement has not been reached and Reid is now set to officially leave on July 1 when his current contract is due to expire, although it is understood a host of clubs are already looking to hold talks with him.
Sky Sports understands that at least three Premier League clubs have expressed an interest in the former Millwall man, whilst a host of Championship clubs are also keen to take him.
Reid has been with West Brom for three years after joining from Blackburn, tweeted his thanks to everyone at the Hawthorns.
"Whatever happens in next few weeks I've had an unbelievable time at West Brom last 3yrs.. Fans, players and staff have all been a pleasure," he wrote.