Mueller's investigators report to Rosenstein, who oversaw the Justice Department's Russia investigation following the recusal of Attorney General Jeff Sessions.
Asked whether Rosenstein might have to recuse himself from the matter, a Department of Justice spokesman said in a statement Tuesday, "As the Deputy Attorney General has said numerous times, if there comes a time when he needs to recuse, he will. However, nothing has changed."
Rosenstein appointed Mueller as special counsel one week after former FBI Director James Comey's firing, and one day after it was revealed that Comey had alleged in an internal memo that President Donald Trump had asked him to end an investigation into former national security adviser Michael Flynn.
The White House initially said Trump had acted on the recommendation of Rosenstein, who wrote a scathing memo about Comey's handling of the Hillary Clinton email investigation.