NBC News reporters further said Mueller had approved Comey to testify publicly.
The former FBI director is expected to testify as early as next week before the US Senate Intelligence Committee, which is conducting one of several investigations into the alleged ties between Trump's election campaign and the Russian government.
Both Trump and multiple Russian officials have denied having ties during the 2016 presidential campaign, and Moscow has repeatedly denied any interference in the election as alleged by the US Intelligence Community.
CNN noted that it is unlikely Comey will give details about the FBI's probe into the matter, but he could discuss his interactions with Trump.
Trump fired Comey on May 10, prompting concerns that the president was attempting to end the investigation.
