A rare bid to break up Alphabet Inc.'s Google is one of the options being considered by the Justice Department after a landmark court ruling found that the company monopolized the online search market, according to people with knowledge of the deliberations.

Regardless, the government will likely seek a ban on the type of exclusive contracts that were at the center of its case against Google. If the Justice Department pushes ahead with a breakup plan, the most likely units for divestment are the Android operating system and Google's web browser Chrome, said the people.

Officials are also looking at trying to force a possible sale of AdWords, the platform the company uses to sell text advertising, one of the people said.

The Justice Department discussions have intensified in the wake of Judge Amit Mehta's Aug. 5 ruling that Google illegally monopolized the markets of online search and search text ads. Google has said it will appeal that decision, but Mehta has ordered both sides to begin plans for the second phase of the case, which will involve the government's proposals for restoring competition, including a possible breakup request.

• Read More