The former No.1 NBA draft pick played last season for the Sydney Kings in the NBL but has since enjoyed some rare downtime in his native Melbourne to ponder his future.

The 36-year-old has been slowed by a nagging back injury but, if still playing next year, presents as a vital piece of the Boomers puzzle alongside core members Patty Mills, Joe Ingles, Aron Baynes and Matthew Dellavedova.

That quartet led Australia's charge at last year's World Cup, their campaign finishing with a heartbreaking fourth place to continue their search for a medal at a major international tournament.

Tokyo's delayed 2021 campaign would be that group's final shot at an Olympic medal together and could be boosted by the addition of NBA All-Star Ben Simmons.

New Boomers coach Brian Goorjian has indicated his desire to have Bogut in Tokyo next year, but knows he must sign a professional contract for next season to be fit to play.

Bogut tweeted on Monday that he would announce where he is signing next season on his new podcast Rogue Bogues.

Kings owner Paul Smith responded to the tweet with one of his own.

"Bogues is his own person, wherever Andrew chooses to play they will be lucky to have him, as were Sydney Kings," he wrote.

Bogut played two seasons with the Kings, collecting the NBL's MVP honours in his first year back after a decorated NBA career that began in 2005.

The centre has played for Australia at three Olympics, missing London's 2012 Games through injury but returning for Rio's 2016 tournament where they finished fourth for the fourth time in an Olympic campaign.

Australian Associated Press