Thompson, 2015 world 200 metre silver medallist, withdrew from the Jamaican 200m final with a hamstring niggle, two days after clocking a world leading 10.70 seconds to win the 100 metres.
Commonwealth Games bronze medallist Russell set a season best of 53.96 seconds on June 2 in Rome, the current third fastest in the world. She did not compete in the trials.
Ludlow Watts, manager of Jamaica's 59 member track and field delegation, said they would be assessed at the team's pre-Olympic training base in Rio de Janeiro by the Jamaica Athletics Administrative Association technical committee.
"These athletes have a deadline of Aug. 8 to prove fitness and that will be done with the medical team by the JAAA," Watts told the Jamaica Gleaner.
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"They will determine whether the athletes are medically fit to compete and, in terms of preparation, if they are ready to compete in the races."
A third athlete with a medical exemption, Hansle Parchment, who won bronze in the 110 metres hurdles at London 2012 and clocked 13.53 seconds just over a week ago, will also need further tests.
"They have to show that they are injury-free or quite relieved of the injury they suffered," Watts said.
Six-time Olympic gold medallist Usain Bolt proved his fitness over 200 metres with a 19.89 second run at the Diamond League meeting in London on July 22.
(Editing by Alison Williams)
