For the American music market, Disney enlisted R&B band All-4-One to record their own rendition of "Someday" for the film's accompanying soundtrack. While the album version of their recording was produced and arranged by William Ross, songwriter Walter Afanasieff was consulted to produce a radio mix of the song which was released by Walt Disney Records and Atlantic Records as the set's first single to US radios on June 10, 1996. The band premiered the song at the New Orleans premiere of The Hunchback of Notre Dame.
In the United Kingdom, all–female trio Eternal lent their vocals to a second version of "Someday". Produced by Simon Climie, it was first released on First Avenue on July 29, 1996 in the UK. The single became the group's eighth non-consecutive top ten entry on the UK Singles Chart and managed to reach the top thirty in Australia and Ireland. In 1997, it appeared on the trio's third studio album Before the Rain.
For the Latin American music market, Disney enlisted Mexican singer Luis Miguel to record the Spanish rendition of "Someday" for the Latin American soundtrack. Miguel's version was included on his fourteenth studio album Nada Es Igual released in the same year. The cover peaked at number 3 on the Hot Latin Songs chart and became his fourth number one song on the Latin Pop Songs chart. A music video was filmed for Miguel's version.