(CNN) Deputy Attorney General Rod Rosenstein has not given special counsel Robert Mueller a certain date by which his investigation into Russian interference in the 2016 election must be completed, a source within the Justice Department familiar with the investigation said.

But speculation that it will wrap up immediately after the November midterm elections is off the mark, the source said. Instead, the probe is expected to wind down by the end of the year.

"Mueller and his team have to provide a confidential report to Rosenstein at the end of the investigation," the source said. "As far as timing, the investigation is obviously ongoing, and I'd expect it to continue well after the midterms."

Rosenstein, who oversees the investigation, on Wednesday called the probe "appropriate and independent," in an interview with The Wall Street Journal, but declined to comment on when it would end.

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