Martin Kobler announced his offer to mediate at a news conference Thursday with a top aide to Prime Minister Nouri al-Maliki.
The camp is run by the People's Mujahedeen Organization of Iran, which opposes Tehran's clerical regime and is critical of al-Maliki.
The government vowed to force political dissidents out of Camp Ashraf after Iraqi forces stormed it on April 8. Several dozen residents were killed in the raid.
At the news conference, al-Maliki aide Gorguis Yacoub said Iraq's Cabinet would consider extending the year-end deadline if a solution can be agreed on quickly.