The Supreme Court will consider Jan. 4 whether to grant review in a trio of cases that could decide whether employers can discriminate against LGBT workers without violating federal civil rights law.

The justices could announce the same day whether they’ll take any of the cases they’ve been asked to hear. It takes four willing justices on the nine-member court for it to grant review.

The question before the court is whether Title VII of the 1964 Civil Rights Act,...