Washington (CNN) White House counselor Kellyanne Conway refused to say Monday whether Deputy Attorney General Rod Rosenstein will keep his job during special counsel Robert Mueller's investigation.

"Can you assure (the American people) that Rosenstein is safe in this job so there's less turnover and less tumult on something as sensitive as this investigation? Is he safe or not?" CNN "New Day" co-anchor Chris Cuomo asked.

"The President makes the decisions around here. You want to say, 'Kellyanne struggles to answer the question' ... Is your job safe at CNN? How do you know that?" Conway replied.

Last week, multiple sources familiar with discussions told CNN that Trump is considering firing Rosenstein , a move that has gained urgency following last week's FBI raids of the office of the President's personal lawyer.

Such an action could potentially further Trump's goal of trying to put greater limits on special counsel Mueller , whose investigation is overseen by Rosenstein in lieu of Attorney General Jeff Sessions, who has recused himself from the investigation.

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