As soon as this summer, The Wall Street Journal reported Friday, the Justice Department is also moving towards bringing a case.
Alphabet shares fell in after-hour trading by about 1.5 per cent.
Google - along with Facebook Inc., Amazon.com Inc. and Apple Inc. - is under a series of probes alleging that tech behemoths use their clout to defend their market share unfairly, including one from the antitrust panel of the House Judiciary Committee.
Google's federal probe focuses on searching, advertising and managing its Android operating system. In 2013 the Federal Trade Commission settled a reprimand against Google's antitrust investigation.
Texas Attorney General Ken Paxton, who is leading the multi-state investigation, said they spoke to companies who said the search and advertising giant had hurt them.
"The coronavirus pandemic has not slowed our antitrust enquiry into Google," he said in a statement. "We are hoping to wrap up the investigation by fall. If we determine that filing is meritful, soon after that we will go to court.
Paxton said he didn't take any punishment off the table in February, including breaking up the giant of search and advertising.
Google said that it would not comment on the potential litigation speculation.
"We continue to engage with Department of Justice and Attorney General Paxton's ongoing investigations and we have no updates or comments on speculation," a Google spokesperson said in an email statement.
The Department of Justice did not immediately respond to a request for comment.
The four tech giants, powerhouses in search and online advertising , social media, online sales, and smartphones, have both caused concern among progressive Democrats and conservative Republicans due to their outsize clout.
It is believed that the Justice Department looks at all four companies while the FTC samples Facebook and Amazon.com. Facebook is also under investigation by dozens of state attorneys general, led by New York.
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