Alyokhina was sentenced to two years in jail last summer for hooliganism charges over her participation in a "punk prayer" protest against Russian President Vladimir Putin at a cathedral in Moscow.
She appeared at a parole hearing via video link on Wednesday, during which she announced she would would start a hunger strike and boycott further proceedings in protest against not being allowed to attend the hearing, RIA Novosti reported.
Meanwhile, Paul McCartney has called for the release of Pussy Riot members in letters he sent to Russian officials.
The former Beatle wrote a letter each in support of Alyokhina, Nadezhda Tolokonnikova and Yekaterina Samutsevicha.
"In the great tradition of fair-mindedness which the Russian people (many of whom are my friends) are famous for, I believe that you granting this request would send a very positive message to all the people who have followed this case," McCartney wrote in a letter supporting Alyokhina.
"I have had a long relationship with the Russian people, and, with this in mind, I am making the following request in a spirit of friendship for my many Russian acquaintances who, like me, believe in treating people -- all people, with compassion and kindness," McCartney wrote regarding Tolokonnikova, as quoted by RIA Novosti.
Samutsevicha was granted a suspended sentence and was released from jail in October 2012.