Verdicts are expected a few weeks later, CAS secretary general Matthieu Reeb told The Associated Press today.
The highest court in sports took over the cases because Russia's track and field federation was suspended by the IAAF in November after allegations of state-sponsored doping made by a World Anti-Doping Agency panel.
The cases include former world heptathlon champion Tatyana Chernova and five race walkers who tested positive for EPO on the same day last June at the national training center at Saransk.
"That would be the best option to be ready for the decision on time before the (Olympic) selection date," Reeb said on the sidelines of the SportAccord conference.
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The IAAF hopes to decide within weeks if Russia's track federation can be reinstated in time for the Rio de Janeiro Games in August.
The hearings could be held in London, Lausanne or Moscow.
Russian sports minister Vitaly Mutko and IAAF President Sebastian Coe both attended the conference today but did not meet.
"This is the person I would like to meet," Mutko told reporters before leaving to return to Moscow, where he will host FIFA President Gianni Infantino on Tuesday.
"We are fulfilling the WADA recommendations," Mutko said through a translator, citing a positive meeting.