Options for that include the site of the Canberra Olympic Pool in Civic - if a rectangular stadium doesn't go there - or at the University of Canberra.

The ACT has been left without an arena following the closure of the AIS Arena in June, which has hosted elite basketball and netball, as well as concerts.

The Canberra Capitals have won back-to-back championships there over the past two WNBL seasons.

While the coronavirus pandemic was part of the reason for the arena's closure, it was also because it needed work done to keep it operational.

It's expected the AIS will look to sell some of its 65-hectare site to fund a major overhaul of their facilities.

Barr said the ACT government will not buy the arena, but wanted Scott Morrison's government to keep it running.

The chief minister said that would give them enough time to be able to build their own venue as part of their infrastructure plan.

"We've determined that the ACT government will not be buying AIS Arena and so what we are looking at is the Commonwealth puts in place a small investment to keep it going for several more years as we contemplate our options for a new arena," Barr told The Canberra Times.

"That's what we're pursuing. We haven't got an answer [yet], but what we have determined is we will not be buying it and we will not be investing money in it.

"It's got a limited life span and if the feds wish to sell it off ultimately as part of their AIS development that's where that's going.

"But we won't be buying a 40-year-old arena that's ultimately too small for our city's future needs."

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Barr said there were several options for a new arena.

There's been plans for a rectangular, football stadium on the current site of the Canberra Olympic Pool for a few years, but it's proving problematic to fit a 25,000-seat venue there.

That could open the way for a smaller arena to be built there instead.

Another option is the University of Canberra, which had plans to build their own basketball stadium on campus - but they've been unable to gain federal funding for the project.

There were also plans to build a soccer stadium as part of the sports complex, which already included the home of the ACT Brumbies.

"The path we've chosen to pursue is to look at a replacement, but that's going to take a few years," Barr said.

"There are a few different options around where that could be.

"One of the potential sites is if you didn't build a football stadium on the Olympic pool site that is a potential site for an arena and that would fit comfortably.

"But there are other sites, including co-locating on the University of Canberra that's also possible."