Cohen's argument is "a dead loser," said former U.S. attorney Harry Litman, who teaches at the UCLA School of Law and continues to practice law. "The search was orthodox and lawful and he has no basis to challenge it," Litman said, based on news reports about the process of obtaining the search warrant.
But even if it turns out that the warrant was acquired on insufficient grounds, Litman said Cohen's strategy for this hearing doesn't hold much water. "Even if it's flagrantly unlawful, the way to challenge that is to keep the government from using the evidence in court against him," Litman said.
Cohen's approach, on the other hand, makes it look like he is trying to temporarily freeze the government's ability to use what it has seized, said Harry Rimm, a partner of the law firm Sullivan & Worcester.
"The argument is likely that this is an unusual case with leaks," where Cohen can't "wait months for a suppression motion because by the time we'd get to a suppression motion in the normal course, Cohen will have suffered terrible harm," Rimm told CNBC in an email.
Cohen is being investigated by federal prosecutors in New York after special counsel Robert Mueller reportedly made a referral to the FBI that led to the warrant. Mueller is investigating potential links between Trump's 2016 presidential campaign and Russia.
Deputy Attorney General Rod Rosenstein personally signed off on the raids, The New York Times reported Tuesday. Legal experts have said the raids on Cohen for information relating to Trump — material normally protected by attorney-client privilege — demonstrate the seriousness of prosecutors' suspicions about Cohen.
Investigators searched for documents relating to the infamous "Access Hollywood" tape in which Trump boasts about sexual harassment, and communications between Trump and Cohen about the tape.
Investigators also sought other records, including those relating to a $130,000 payment made by Cohen to porn star Stormy Daniels as part of a hush deal about an alleged sexual encounter with Trump a decade earlier. They also reportedly looked for documents in Cohen's possession related to payments made to another woman who claims she had an affair with Trump, Playboy model Karen McDougal.
This is a developing story. Please check back for updates.