The club is one six from the Premier League and Championship to apply to join the pilot project, the Express & Star understands.
Wolves became the first club in the top flight to instal rail seating two years ago when a section of the South Bank was converted.
They have since been followed by Chelsea, Liverpool, Manchester City, Manchester United and Tottenham in introducing rail-seating.
The programme, which will allow those clubs whose applications are successful to offer a licensed safe standing area, was announced last month by the Sports Grounds Safety Authority.
It will end a blanket ban on standing in the top two tiers of English football which has been in place for more than 25 years.
An SGSA spokesperson said: “Applications to become early adopters of licensed standing in seated areas for the 2021-22 season are now closed.
“The SGSA is now reviewing the applications and will provide advice and recommendations to the Department for Digital, Culture, Media and Sport (DCMS) for final decision.”
Standing areas in the top two tiers of English football were outlawed in the wake of the 1989 Hillsborough disaster, which led to the deaths of 97 Liverpool fans.
The introduction of the licensed standing areas follows a commitment by the Government in its 2019 General Election manifesto, and it is a move which has cross-party support.