The Pro 12 champions currently play in The Sportsgrounds
Connacht Rugby hierarchy are considering moving the team to Eamonn Deacy Park, as talks to increase The Sportsgrounds' capacity have stalled.
Pat Lam's side won the Pro 12 last season, with Connacht's final league games selling out, despite the club claiming they could have sold more tickets. The capacity of The Sportsgrounds is currently around 8,000.
Connacht have played in the venue since the 1920s. It is currently owned by The Galway Agricultural & Sports Society Ltd and is leased by both Connacht Rugby and Bord na gCon.
The Irish Independent claim that Connacht representatives are to meet members of the Galway FA (the owners of the ground) next week. Preliminary discussions have reportedly already taken place with FAI Chief Executive John Delaney.
Speaking to Newstalk earlier this month, Connacht Chief Executive Willie Ruane said that negotiations regarding a future Connacht stadium are "very live right now".
"This has been our home for a long time - you’d love to try to achieve something here in the Sportsground if that’s doable - but it has to be the right type of development."
"We’ve done a lot of work in terms of examining all the different options. There’s one or two that are viable that we’re not really in a position to talk about publicly at the moment, but we are looking very closely at them"
Connacht begin the defence of their Pro 12 title, against Glasgow in The Sportsgrounds this weekend.