Time Warner shares fell Thursday after a newspaper reported that the Department of Justice is considering an antitrust lawsuit to block AT&T's acquisition of the media company.

Time Warner share price was down 4.1 percent after The Wall Street Journal reported that the department's antitrust division is preparing for litigation in case it decides to sue to block the deal. AT&T's stock was down 1.2 percent.

At the same time, the department and the companies are discussing possible terms that would allow the deal to receive the government's approval, the Journal reported, citing people familiar with the matter.

AT&T representatives have met with Justice officials in recent weeks, and the department hasn't made a final decision, but the two sides aren't close to an agreement, the Journal's sources said.

"When the DOJ reviews any transaction, it is common and expected for both sides to prepare for all possible scenarios," AT&T said in a statement. "For over 40 years, vertical mergers like this one have always been approved because they benefit consumers without removing any competitors from the market. While we won't comment on our discussions with DOJ, we see no reason in the law or the facts why this transaction should be an exception."

Time Warner and the Department of Justice declined comment.

AT&T reached an agreement to buy Time Warner for more than $85 billion last October. In July, sources told CNBC the deal could close in as soon as 60 days.

Read the full Wall Street Journal story here.