There is no available evidence in the provided sources confirming that Lev Parnas has publicly stated that President Trump is actively seeking to rig future elections to keep the GOP in power.
Fact Check: "Lev Parnas, father of Aaron Parnas, convict & former confidante caught in scheme that got Trump impeached, says the President is actively seeking to rig future elections to keep GOP in power"

FactVerify
Source: factverify.com
What the Evidence Shows
The claim involves several components: first, that Lev Parnas is the father of Aaron Parnas; second, that Lev Parnas is a convict and former confidante involved in the scheme that led to Trump's impeachment; and third, that Lev Parnas has stated the President is actively seeking to rig future elections to maintain GOP control. The sources confirm that Lev Parnas is indeed a convicted associate of Rudy Giuliani who was involved in activities related to the Trump-Ukraine scandal, which contributed to Trump's first impeachment.
It is also confirmed that Aaron Parnas is his son. However, none of the sources provide any information or direct quotes from Lev Parnas making claims about President Trump actively seeking to rig future elections. The search results focus on definitions of 'fact' and on Lev Parnas's conviction and sentencing but do not include any statements or verified reports about his views or allegations regarding election rigging by Trump.
Without direct evidence or credible reporting on this specific statement by Lev Parnas, the claim cannot be verified based on the provided information.