A spokeswoman for the company said that AT&T provided all information requested by Mueller's office in November and December of last year.
"A few weeks later, our consulting contract with Cohen expired at the end of the year. Since then, we have received no additional questions from the Special Counsel's office and consider the matter closed," AT&T said in its statement.
Earlier Wednesday, a source told CNBC that the telecommunications giant paid Cohen up to $600,000 as part of a consulting contract to get insight into Trump's thinking. The source said that the payment to Cohen was for "actual work done," adding: "And it wasn't to pay for access to the president."
"It was to pay for an understanding of the inner workings of Trump, his thought process, how he likes to operate, how he likes to make decisions, how he processes information," the source said.
"And how he thinks about the big issues," the source added.
AT&T told employees Wednesday in a memo that it had hired Cohen as one of several consultants to "help us understand how the President and his administration might approach a wide range of policy issues important to the company, including regulatory reform at the FCC, corporate tax reform and antitrust enforcement."
AT&T is trying to buy media conglomerate Time Warner for $85 billion. The Justice Department opposes the deal on antitrust grounds, and now the companies are awaiting a verdict from a federal judge.
Another company that paid Cohen, Swiss drug giant Novartis, signed a consulting contract with him in February 2017 after he approached the company and promised "access" to the new Trump administration, according to NBC News, citing a Novartis official.
Novartis revealed earlier Wednesday that it had paid Cohen $1.2 million for consulting work related to health-care policy.
The company said it continued paying the president's personal lawyer under that one-year contract despite finding out within just a month or so that Cohen was unable to do the work expected.
On Tuesday, a bombshell report released by the lawyer for porn star Stormy Daniels said that Cohen, Trump's longtime attorney and confidant, had received a series of suspicious payments from several companies, including AT&T and Novartis.
Daniels' lawyer, Michael Avenatti, had said Cohen's shell company, Essential Consultants, had received a total of $200,000 in four monthly installment payments of $50,000 from AT&T.
But under the contract that AT&T had with Cohen, the lawyer may have been paid up to $600,000, according to the source who spoke with CNBC.
Essential Consultants was set up by Cohen in October 2016, and soon afterward it paid Daniels $130,000 in a hush-money deal in which she agreed not to discuss an alleged sexual encounter with Trump. The White House denies the tryst occurred.
AT&T on Tuesday night had told CNBC that Cohen's company "was one of several firms we engaged in early 2017 to provide insights into understanding the new administration."
In a memo sent to its employees on Wednesday, AT&T said:
Late yesterday, many media outlets reported that in 2017, AT&T hired Michael Cohen, a former lawyer with the Trump Organization. We want you to know the facts.
In early 2017, as President Trump was taking office, we hired several consultants to help us understand how the President and his administration might approach a wide range of policy issues important to the company, including regulatory reform at the FCC, corporate tax reform and antitrust enforcement. Companies often hire consultants for these purposes, especially at the beginning of a new Presidential Administration, and we have done so in previous Administrations, as well.
Cohen was one of those consultants. Cohen did no legal or lobbying work for us, and our contract with Cohen expired at the end of its term in December 2017. It was not until the following month in January 2018 that the media first reported, and AT&T first became aware of, the current controversy surrounding Cohen.
That last line about "the current controversy" seems to refer to Cohen's entanglement with Daniels. He is also under criminal investigation by federal prosecutors in New York, who are probing his business dealings.
Yet Cohen has been under heavy media scrutiny since early January 2017, around the time AT&T says it hired Cohen. At the time, BuzzFeed published the so-called "Steele Dossier," which alleged a conspiracy between the Trump campaign and Russia to influence the 2016 election.
Cohen is mentioned throughout that memo, which received widespread media attention. The memo claims Cohen attended a "secret liaison with the Kremlin" in Prague, a claim that Cohen strenuously denied.
Cohen had sued BuzzFeed for libel but dropped that suit last month.