Russia was drawn to face Poland in a World Cup qualifying play-off semi-final, but the Poles received a bye and then reached the finals starting November 21st by beating Sweden.
"The process will soon be closed," said CAS which on March 18th refused to overturn the ban.
The Russian Federation said it would continue its appeal against UEFA, who have banned Russian clubs from continental competitions.
CAS said it would not lift the UEFA ban on Russian clubs and is has as yet to decide upon a date for a final ruling.