"Everything will be decided in September. It is impossible to say for certain but I think she will start playing again by January," Tarpishchev was quoted as saying by the TASS news agency on Monday.
Former world number one Sharapova was suspended following a positive test for the banned drug meldonium during January's Australian Open.
The 29-year-old was named in Russia's official entry list for the Olympic Games in Rio de Janeiro but the Court of Arbitration for Sport (CAS) decided in July to defer its decision on her appeal against the ban until September 19.
Sharapova is seeking to have her suspension, which was handed down by the International Tennis Federation (ITF) in June, wiped out or reduced.
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The postponement of the ruling came because Sharapova and the ITF needed more time to "complete and respond to their respective evidentiary submissions", the CAS said in a statement.
(Reporting by Dmitriy Rogovitskiy; Editing by Tony Jimenez)
