Special counsel Robert Mueller’s office asked a federal judge to grant immunity to five witnesses expected to testify against Paul Manafort, providing a window into the team’s strategy for a trial expected to begin next week.

In a set of filings Tuesday, Mr. Mueller’s prosecutors said they had five potential witnesses against Mr. Manafort, President Donald Trump’s former campaign chairman, who have refused to testify based on their Fifth Amendment right against incriminating themselves. Prosecutors asked for the court to compel...