The RDS has submitted a planning application for the €26m redevelopment of its Anglesea Stand, according to the Irish Independent.
If approved by Dublin City Council, the main arena's capacity would rise from 18,500 to 21,000.
A consortium of Grimshaw / Newenham Mulligan Architects won the international competition for the redevelopment.
The RDS has since been working with the design team to meet the specific requirements of Leinster Rugby, the Dublin Horse Show and other commercial considerations.
Michael Duffy, CEO of the RDS, said:
"Designing a stadium to meet the unique design requirements of the RDS Main Arena is a complex and challenging task.
"We have today submitted a planning application for a redeveloped Anglesea Stand which will create a top class experience for visitors and positively impact on the Dublin Horse Show, Leinster Rugby and any other events held in the Main Arena."
Mick Dawson, CEO of Leinster Rugby, added:
"This has taken a huge amount of work from all concerned and the RDS have gone about it the right way.
"It is great to be able to take that next step. It is welcome news for all involved with Leinster Rugby but in particular for our season ticket holders who continue to support us in great numbers but are eager to see how this all develops.
"I think this is a very positive step as we look towards developing the RDS Arena into the best in class offering that we all know it can be."