"No, I don't [plan on firing Rosenstein]," Trump said when asked about such a possibility, as quoted in the USA Today newspaper.
The president added that he got along "very well" with the deputy attorney general.
According to the media outlet, Rosenstein was summoned to the White House two weeks ago, expecting to be let go.
Trump has reportedly criticized Rosenstein over appointing Robert Mueller a special counsel leading a probe into alleged Russian meddling in the 2016 US election.
Russia has repeatedly refuted all allegations of tampering with the US elections, stressing that the claims remained unsubstantiated.