WASHINGTON—The Justice Department has signaled it is willing to approve Sinclair Broadcast Group Inc.’s planned takeover of Tribune Media Co. but with a condition: It wants the companies to sell off roughly a dozen television stations.

The department told the companies the deal as currently structured raises antitrust problems and that 12 to 13 station sales are necessary to alleviate concerns about competition in markets where a combined Sinclair-Tribune would otherwise have a commanding presence, according to people familiar...