Prosecutors want to keep him in prison while they probe his alleged involvement in the 2005 disappearance of Madeleine McCann.
Brueckner was extradited from Portugal to Germany in 2017, where he was jailed for sex offences against children.
He was released from prison in August 2018, but officials put him under surveillance and told him to report in once a month.
Instead he fled the country.
Madeleine McCann disappeared in the Algarve in 2005. Photo / Supplied
He was arrested in Milan and extradited to Germany, where he is jailed for drug offences dating back to 2011. He's also received a seven-year sentence for the rape of an elderly woman.
Portuguese police last week reportedly launched a search for Madeleine McCann's body in the Algarve.
The search begun after authorities found "fundamental evidence" they say is linked to Brueckner, the prime suspect.