Rosenstein then determines whether to allow Mueller to proceed or to assign the matter elsewhere.
A warrant requires high-level approval within the Justice Department, and agency guidelines impose additional hurdles when the search target is an attorney.
Cohen has denied wrongdoing.
In the weeks since, the media-savvy Avenatti has helped keep the spotlight on the case, shepherding his client through a high-stakes 60 Minutes interview, sparring with one of Cohen's lawyers on cable news, taunting Cohen and Trump on Twitter and hinting at startling new developments. It's not unheard of to execute a search warrant on an attorney's office, but executing such a warrant on the personal attorney of the USA president is something else altogether, perhaps even historic.
Assistant U.S. Attorney Tom McKay accused Cohen of trying to invoking "wildly overbroad" claims of attorney-client privilege to avoid the disclosure of thousands of allegedly privileged communications related to the president and other cases. But it doesn't apply under the "crime-fraud exception", which strips those protections if the communication involves an attorney and client furthering criminal activity.
Meanwhile, The Washington Times reported that Cohen is planning to invoke his Fifth Amendment right against self-incrimination in Daniels' defamation lawsuit against him. Still, Senate Judiciary Committee Chairman Chuck Grassley, R-Iowa, told reporters Wednesday the legislation is expected to come up for a committee vote, possibly as soon as next week.
"It becomes an issue when they either exceed the limits on contributions that can be made to candidates or political parties or PACs, or when they are not properly disclosed", he explained.
Trump's Deputy Attorney General, Rod Rosenstein, reportedly signed off on the search warrant.
Uncertainty over exactly what Federal Bureau of Investigation agents seized from Cohen comes as Trump faces an intensifying probe by Special Counsel Robert Mueller into whether his presidential campaign colluded with Russian Federation.More news: West Brom's Jay Rodriguez cleared of alleged racial abuse
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But Mueller did have a hand in instigating the raids.
The official added that the President's cooperation should be proportional to the courtesy he receives from the special counsel.
Several former officials at the Federal Election Commission have said the payment appears to be a violation of campaign finance laws, and multiple Washington-based groups have filed complaints with the FEC, urging it to investigate.
The request indicates that prosecutors may have an interest in specific financial transactions that Cohen undertook while using his taxi business as collateral. Email communications could be of great concern if they include statements Trump made under the presumption his words would never go public. "I have assurances that it's not because I've been talking to people in the White House about it", Ryan said. Some senators fear doing so could lead to a constitutional crisis.
Aides said Trump was fuming on Tuesday over the raids but his future course of action remained unclear.
In an extraordinary turn, the man known as Donald Trump's long-time fixer is facing intensifying scrutiny by US authorities, a situation which could pose new legal risks for the President himself.
Cohen "would be as damaging a witness against Donald Trump as any witness Mueller could secure".