A CAS source told the news agency TASS that a hearing into cases of all 32 applicants will be held on Wednesday.
"The panel's decisions are expected to be announced either late in the evening of 8 February 2018 or in the morning of 9 February 2018", Cas said.
"All our documents and words were heard."The Russians are seeking to overturn the International Olympic Committee's decision not to invite them to the games".
CAS is also handling appeals of Russians, including Olympic champion skater Viktor Ahn, who had not been named in the doping investigations or had any prior doping offences but were still not invited due to doping suspicions by the IOC.
The group of 32 athletes including six-time Olympic gold medalist Viktor Ahn, three former National Hockey League players and world biathlon champion Anton Shipulin failed to pass mandatory IOC vetting, imposed as a result of Russian doping at the 2014 Games.
The ongoing fall-out of the Russian Federation doping scandal, which culminated as it hosted the Sochi 2014 Winter Olympics, has overshadowed other aspects of Pyeongchang, including the participation of North Korea.
The Court of Arbitration for Sport says the 13 athletes and two coaches include cross-country ski gold medalist Alexander Legkov and skeleton gold medalist Alexander Tretiakov, as well as speedskating silver medalist Olga Fatkulina. "This should draw a line under this damaging episode and serve as a catalyst for a more effective anti-doping system led by WADA".
John Coates, the Australian IOC member who also oversees CAS operations, said Tuesday that the 32 had also filed appeals in Swiss courts, but didn't give details.
The cases have been adjourned until Thursday.After revelations of a state-sponsored doping conspiracy, the International Olympic Committee suspended Russia in December but allowed a large group of "clean" Russian athletes to compete under a neutral flag. If they win, it would force the IOC to accept athletes it considers to be linked to doping offenses.The Russian team is formally banned, so they would have to compete as "Olympic Athletes from Russia" in neutral uniforms under the Olympic flag.
They were all banned a year ago over doping at the 2014 Olympics in Sochi, but those verdicts were overturned at the CAS last week.
On Wednesday afternoon, the CAS will also be hearing the appeal of 32 other Russian athletes who were not invited by the IOC. As a result of the probe, a total of 43 Russian athletes were handed lifetime bans from Olympic competitions and stripped of their medals won in Sochi - despite never having tested positive for doping.
Bach, asked whether he had presided over a "fiasco", said this week's International Olympic Committee session had overwhelmingly backed a vote of confidence in the handling of the crisis. Hundreds more have been barred, and many have gone to court seeking entry and causing last-minute chaos.