Washington (CNN) The midterm elections this year might be haunted by allegations of Russian meddling in Donald Trump's presidential campaign, after a federal judge said Tuesday that Trump campaign officials Paul Manafort and Rick Gates may face their criminal trial just before November.

Judge Amy Berman Jackson suggested at a hearing Tuesday morning that the trial could start in September or October, meaning it could potentially end weeks or days before the midterm election.

Prosecutors from Robert Mueller's special counsel office asked for three weeks to present their side of the case at the trial.

The judge refrained from setting a firm date. Previously, Berman Jackson and the prosecution had sought a May start for the trial. That date was too soon, she said, because Mueller's office was still turning over evidence to the defense team -- some 640,000 documents and other items as of this week, prosecutors said.

Statements from the defense teams addressing their indictments will be due by the end of February, and both sides will argue about them through March, the judge said.

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