Cummins, who has not played an international game in the short format since June 2024, was rested from the final two Ashes games against England to manage his back issues, only playing in the third test in the series.
The pacer will undergo final scans later in the month to determine his participation in the World Cup, Cricket Australia said. The teams have until January 31 to name their final squads.
Hazlewood was ruled out of the entire Ashes series with an injury in the Achilles' region while recovering from a hamstring strain, while David picked up a fresh hamstring injury in the Big Bash League (BBL) on Boxing Day.
“They are tracking well and we are confident they will be available for the World Cup," Australian chair of selectors George Bailey said.
Australia also handed surprise call-ups to left-armer spinners Matt Kuhnemann and Cooper Connolly, who have just one T20 wicket between them.
They join experienced leg-spinner Adam Zampa, with Glenn Maxwell and Matthew Short offering additional spin support.
“This is a preliminary squad so should changes need to be made they will be made ahead of the support period," Bailey said.
Connolly has been in sublime form with the bat in the BBL this year with 170 runs in four games at a strike rate of 166.
Australia, who will be playing their group games in Sri Lanka, will be led by Mitchell Marsh as captain, and will kick off their World Cup campaign against Ireland on February 11.
The Aussies have until January 31 to make any changes to their provisional squad without cause or reason. Following that date, only injury replacements will be permitted.
Australia provisional T20 World Cup squad:
Mitch Marsh (c), Xavier Bartlett, Cooper Connolly, Pat Cummins, Tim David, Nathan Ellis, Cameron Green, Josh Hazlewood, Travis Head, Josh Inglis, Matt Kuhnemann, Glenn Maxwell, Matt Short, Marcus Stoinis, Adam Zampa