Justice Department antitrust enforcement staff have told T-Mobile US Inc. and Sprint Corp. that their planned merger is unlikely to be approved as currently structured, according to people familiar with the matter, casting doubt on the fate of the $26 billion deal.

The nation’s third- and fourth-biggest carriers by subscribers are facing challenges on several fronts, but their most immediate hurdle comes from the Justice Department’s antitrust division, which is considering whether the deal would present an unacceptable threat...