The jetliner crashed in Ukraine in pro-Russian rebel-held territory on July 17, 2014, killing all 298 people on board, including 28 Australians.
The aircraft, which was en route from Amsterdam to Kuala Lumpur, was shot down by a Russian-made surface-to-air missile, the Dutch Safety Board concluded in its final report late last year.
Fighting was raging in eastern Ukraine between Russian-backed separatists and Ukrainian government forces when the aircraft was downed and many Western experts and governments blamed the rebels.
Australia's Fairfax media reported on Saturday that 33 next of kin were of victims named in an application by Sydney law firm LHD Lawyers, representing people from Australia, New Zealand and Malaysia.
Reuters could not immediately reach LHD Lawyers for comment.
The application was filed on May 9 and names the Russian Federation and Putin as respondents and seeks $10 million in compensation per passenger, the report said.
The Dutch Safety Board, which was not empowered to address questions of responsibility, did not point the finger at any group or party for launching the missile