A longtime Putin ally, Kudrin, 51, resigned as finance minister and deputy prime minister last year following a row with President Dmitry Medvedev over budget issues including rising defense spending.
"I have been offered several positions over the past year, but I refused to accept them because the [state] policies I disagreed with remain unchanged,” Kudrin said in an interview with Echo Moskvy radio. He did not clarify on who had offered him the posts.
He added that as long as Dmitry Medvedev remains prime minister, the government is unlikely to change its course.
Kudrin made a partial return to national politics in April with the formal establishment of his Civil Initiatives Fund, an advisory body on political and economic issues under President Vladimir Putin.
The former finance minister has attended demonstrations held by the protest movement that swept Russia following the December 4 parliamentary elections, triggered by allegations of widespread vote fraud in favor of the pro-Kremlin United Russia party.
He repeatedly indicated he was ready to mediate in talks between the Kremlin and opposition activists, but has not received any offers to lead an opposition party or movement so far.