When it comes to President Trump’s legal health and welfare, few recent events have borne as much potential risk as the extraordinary raids that federal agents conducted last month on Michael D. Cohen, his longtime lawyer and fixer. Seizing boxes of documents and about a dozen cellphones, iPads and computers, the agents were looking for evidence that Mr. Cohen broke the law in his wide-ranging business deals — among them, hush-money payments that he made to women who claimed they had affairs with Mr. Trump.

While it is possible that the early-morning searches could eventually result in criminal charges, the broader inquiry that led to them is, for now, bogged down in two legal disputes about the cache of materials that was seized. On Wednesday morning, five sets of lawyers in the case are expected to appear in Federal District Court in Manhattan to work toward resolving both of the quarrels — negotiations that will affect how the case moves forward.

The most important (and, perhaps, most complicated) argument concerns the question of whether any of the paperwork or data swept up in the raids may be protected by the lawyer-client privilege that Mr. Cohen shared with Mr. Trump. After the raids, Mr. Cohen’s lawyers asked the judge in the case, Kimba M. Wood, for an order to prevent the government from making that decision, saying that they and lawyers for Mr. Trump were best suited to determine the issue of privilege. Calling that request unusual, federal prosecutors told Judge Wood that, under normal circumstances, a team of their colleagues who were not directly involved in the matter would be the ones to sort through the materials and set to the side any that contained privileged information.

But Judge Wood decided to appoint an independent arbiter, or a so-called special master, to review the materials. And for the last four weeks or so, the special master, Barbara S. Jones, a former federal judge, has been doing just that, slowly returning to the government those documents that are not protected by lawyer-client privilege.