The plan has the support of WestpacTrust Stadium, Lambton Harbour Management and the Wellington Chamber of Commerce.
It would be as big as two or three rugby fields and accommodate the needs of indoor netball, basketball, table tennis and gymnastics, amongst others.
At present, the different sports facilities were "generally inadequate" and some indoor sports found funding more difficult than high-profile outdoor ones, Mr Graham said.
The venue, expected to cost between $10 million and $30 million, would provide space for interschool and interclub events, as well as regional, national and even international events, while being complementary to the Events Centre.
Representatives of Sport Wellington are seeking the $60,000 required for a feasibility study into the multimillion-dollar sports venue.
The award-winning WestpacTrust Stadium may be joined by an indoor sports venue.
