The Director of Public Prosecutions made the application in the Victorian Court of Appeal on Tuesday, five months after NSW Supreme Court Justice Elizabeth Fullerton published her findings.
She ruled four Victoria Police officers had engaged in a joint criminal enterprise to pervert the course of justice through their work with Ms Gobbo.
Two of those officers can now be named as Jim O'Brien, the head of the former Purana taskforce formed to investigate Melbourne's gangland war, and Inspector Dale Flynn after they lost a further bid to suppress their names.
The other two officers were part of the source development unit and are protected by pseudonyms.
Justice Fullerton also found Victorian Supreme Court Justice John Champion, the former director of public prosecutions, made an error in judgment.
Justice Champion learnt of Ms Gobbo's previous informer status during a 2012 meeting with senior police but he did not take steps to advise Ms Gobbo's clients of her role until 2016, Justice Fullerton found.
"I was not satisfied that the necessary degree of rigour was applied by the director in this case," her findings read.
The rulings were the first step in Mokbel's appeal against his drug trafficking and importation convictions.
Mokbel, who was released on bail on April 4, said he was represented by Ms Gobbo while she was giving information against him to Victoria Police.
Ms Gobbo, a registered police informer from 2005 to 2009, was acting as Mokbel's lawyer for four years before he fled to Greece in 2006 and continued to advise him when he was extradited in 2008.
Mokbel pleaded guilty to two counts of trafficking a drug of dependence for trafficking MDMA and methamphetamine in April 2011, after striking a deal with prosecutors.
He did not find out about Ms Gobbo's status as an informer until the High Court lifted gag orders in 2018.
Justice Fullerton was critical of police's failure to obtain legal advice before Ms Gobbo was registered as an informer and on whether her clients should have been told.
She said ex-chief commissioner Simon Overland's evidence on this was "unworthy of acceptance".
Mokbel's full appeal hearing is expected to be heard before the end of the year.
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