Walt Disney Co. has re-engaged in discussions with 21st Century Fox to purchase some of the media giant’s assets, and Comcast Corp. remains in the mix, with deal talks gaining momentum, according to people familiar with the situation.

The talks center on the Twentieth Century Fox movie and TV studio, international assets such as Fox’s 39% holding in U.K. satellite TV provider Sky PLC and India’s Star TV, along with some U.S. cable networks. Fox News, the Fox broadcast network and sports network FS1 aren’t expected to be sold...