Maduro is due to be re-inaugurated on Friday.
Gonzalez, now in exile in Spain, says the presidential election in July was rigged and says he himself won it.
The opposition has called for mass protests this week and Maduro’s government is offering a $100,000 (£81,000) reward for information leading to Gonzalez’s arrest.
The vote counts – a detailed official breakdown of votes from each polling station – have been at the heart of the dispute over who won the election.
The government’s National Electoral Council declared Maduro the winner, but could not provide tallies to back up its claim.
The opposition, which has collected and published more than 80% of the vote counts with the help of accredited election witnesses, says they prove that Gonzalez was a landslide victory.
UN Human Rights Committee Venezuela ordered in December “refrain from destroying” voting records in the July elections.
