The new arena, which would be built on a site currently used as a training pitch, has been earmarked as Edinburgh Rugby’s new home.
According to the application the stadium will incorporate a new 3G playing surface and four covered stands around the pitch.
Edinburgh will play their home matches of the 2018/19 season at BT Murrayfield, with hopes the team will be able to host matches at the new venue from the start of the 2019/20 campaign.
Scottish Rugby are understood to be open to making the space available for “other users from the wider rugby community in Scotland, and the possibility of other sports as well”.
Scottish Rugby’s Chief Operating Officer Dominic McKay said: “We are incredibly excited to be in a position to be able to submit this application to give Edinburgh a new home.
“After many years of exhausting all the potential stadium and playing ground options for Edinburgh in the local area, we have taken the initiative and will be investing ourselves to develop a venue that can help the team to grow and provide a great spectator experience.
“We are fortunate to have space within the BT Murrayfield campus to comfortably accommodate this planned new facility and retain practice pitches for all elements of rugby.”
Edinburgh Rugby Managing Director Jonny Petrie said: “Having just enjoyed one of the club’s most positive seasons in recent times on the pitch, it is hugely exciting to announce our intentions to move to a new purpose-built new home.
“It has been a consistent challenge to grow the club without our own ground and we now have developed plans that meet the needs of our fans and reflect the direction we want the team to be moving in.”
Edinburgh Head Coach Richard Cockerill welcomed the new project, adding: “I’ve said right from the start that Edinburgh has a lot of potential but it had lacked a strong culture and sense of identity.
“What is exciting about this new project is that as a club, as players, staff and fans we could have a home that we can begin to build something from. It will give us a focal point, excellent facilities and a chance to move the club forward both on and off the pitch.”
The Scotland national team and other representative squads currently use the Oriam facility for training purposes and while the on-site facilities at BT Murrayfield are in need of upgrading, it is understood an area housing an existing 3G pitch to the west of the stadium will be used for the new arena.