The chatter about Steve Nash’s future whipped up in earnest over the weekend, which isn’t surprising for two reasons:

1.Free agency is officially less than a month away now that we’re into June.

2.Nash and another NBA senior citizen -- Boston’s Kevin Garnett –--would appear to be the two most attractive unrestricted free agents on the 2012 market not named Deron Williams ... since no one expects Tim Duncan to give leaving San Antonio one millisecond of thought when Duncan theoretically joins Nash and KG on the open market July 1.

Nash himself, I’m told, is still days away from giving his future deep thought. He said many times late in the regular season that he’ll listen to any pitch that comes this summer, hoping that the next contract he signs -- preferably for three seasons -- will be his last. But he admitted last month at a press conference in Toronto that he hadn’t even started the process.

More, then, is known about the teams chasing Nash. It’s a list that still starts with the Phoenix Suns, who cling to the hope that they can keep the most beloved player in franchise history, but it’s also destined to be a longer list than you think once free agency actually starts, since Nash is seen around the league as far more gettable than D-Will.

Sources briefed on the matter told ESPN.com that the three teams with salary-cap space best positioned to make a credible run at the 38-year-old, at this early juncture, are Portland, Toronto and Brooklyn (should the Nets lose D-Will).

New York and Miami are also frequently mentioned as potential Nash destinations, but neither the Knicks nor the Heat have the requisite cap room to make a serious bid. The Blazers, by contrast, have coveted Nash for years in trades and will finally have the financial flexibility to chase him, offering the closest proximity to Nash’s Vancouver roots than anywhere else on the NBA map among other perks. Sources say that the Raptors, meanwhile, will be determined suitors in the Nash Sweepstakes, with a serious offer forthcoming to try to bring the newly installed general manager of Canada’s national team back to home soil after 16 seasons south of the border with the Suns and Mavericks.

Also: CSNChicago.com reported Sunday that the Chicago Bulls intend to join the Knicks and Heat on the list of glamour teams that will take a long-shot run at Nash. You can go ahead and put Dallas in that club, too, should the Mavericks fail in their attempt to bring DFW-area native D-Will home.

The New York Daily News, furthermore, reports that the Suns plan to “go all out” for Williams if they end up losing Nash. The safest forecast of them all: This won’t be the last story that mentions both Williams and Nash, since they’re two of the certifiable stars -- albeit at vastly different stages of their career -- in a free-agent class with precious few of them.