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Attorney General Jeff Sessions is not backing down this time.
"To the extent a matter comes to the attention of his office that may warrant consideration of recusal, the attorney general would review the issue and consult with the appropriate Department ethics experts", it said.
With Sessions not recusing himself, it means the once-top Trump campaign adviser could be notified of the status of the Cohen probe and engage in decisions surrounding the case.
It's hard to see how the Cohen investigation wouldn't be related to the campaign.
Trump launched an attack against the New York Times on Twitter on Saturday, after the Pulitzer Prize-winning reporter Maggie Haberman wrote about the pressure Cohen was facing to testify against Trump, in order to avoid expensive legal fees and potential criminal charges.
He has since been the subject of Trump's wrath in a series of tweets and public comments.
Leahy also asked Sessions whether he had been briefed on or made decisions affecting the investigation into Cohen, and whether he discussed the investigation with the president.
Sessions's decision to remain involved in the Cohen investigation could put him in a position for Trump to ask him to disclose details and information about the probe, Bloomberg noted.
That "raises the possibility" that Cohen broke campaign finance laws, according to Leahy.
Sessions' original recusal caused him to step aside from the FBI's investigation into the Trump campaign's contacts with Russian Federation. Sessions' recusal enraged Trump, who has publicly berated his attorney general for failing to protect him from the probe.
The president also fired off several other tweets on Saturday attacking the media and fired Federal Bureau of Investigation director James Comey and announcing that he is considering offering a posthumous pardon to boxing's first black heavyweight champion more than 100 years after the late Jack Johnson was convicted by all-white jury of accompanying a white woman across state lines. In a letter a year ago, the Justice Department acknowledged that Sessions played a role in responding to congressional Republicans' calls for the department to investigate issues related to Hillary Clinton, when it boasted he personally "directed senior federal prosecutors" to undertake such a review.
Leahy asserts that the Cohen probe is likely related to the 2016 presidential campaign.
Trump denounced the raid as "an attack on what we all stand for" and repeated that it was a "terrible mistake" for Sessions to recuse himself from the Mueller probe.
The prospect of Trump pardoning Cohen has been a source of growing speculation since a Trump tweet over the weekend.
By staying involved in the Cohen probe, Sessions is entitled to briefings on the status of the investigation, which is being conducted by the U.S. Attorney's Office of the Southern District of NY. "Even though they are not speaking right now, messages were sent".
In his letter, Leahy said that last March, Sessions announced he was recusing himself from investigations into "any matters related in any way to the campaigns" for president.