Michael D. Cohen, President Trump’s longtime personal fixer, will soon be parting from the lawyers who are representing him in a potentially damaging and wide-ranging federal investigation into his business dealings, according to two people familiar with the case.

Prosecutors conducting the inquiry have not yet approached Mr. Cohen to seek his cooperation, according to two people briefed on the case. But as the investigation continues, and with Mr. Cohen’s legal team in flux, the pressure on him to cooperate with the government may well intensify.

Mr. Cohen’s current lawyers — a three-man team from the firm of McDermott Will & Emery — are expected to stay with him for at least the rest of the week as they struggle to complete a laborious review of a trove of documents and data files seized from their client in a series of extraordinary early-morning raids two months ago. But after that review is finished, Mr. Cohen will seek new legal counsel, the people familiar with his case said.

The dispute between Mr. Cohen and his lawyers involves the payment of his legal bills, part of which are being financed by the Trump family. Mr. Cohen has also had more longstanding concerns about the lawyers: As his case moves forward, possibly toward criminal charges, he has been thinking for some time about hiring a new legal team with stronger relationships with the federal prosecutors’ office in New York that is leading the investigation, according to the people briefed on the matter.