The nominations are expected to upset church conservatives.
The Diocese of Los Angeles represents 70,000 Episcopalians in six counties, and is considered to be one of the most liberal in the U.S. church of 2.1 million members.
Its bishop, the Rt. Rev. J. Jon Bruno, is an advocate of gays rights in the church.
"I affirm each and every one of these candidates and am pleased at the wide diversity they offer this diocese," Bruno said in a statement.
Dozens of more traditional churches and four dioceses broke away last year because they opposed the 2003 consecration of a partnered gay bishop in New Hampshire.
U.S. church leaders had promised to be cautious before allowing more gay bishops, but at last month's convention in Anaheim, they voted to open "any ordained ministry" to gays and lesbians and to consider rites of blessing for same-sex couples, the Times reported.
The other bishop nominees include the Rev. Canon Diane M. Jardine Bruce of St. Clement's by-the-Sea Episcopal Church in San Clemente; the Rev. Zelda M. Kennedy of All Saints Episcopal Church in Pasadena; the Rev. Irineo Martir Vasquez of St. George's Episcopal Church in Hawthorne; and the Rev. Silvestre E. Romero of St. Philip's Episcopal Church in San Jose.
Leaders in the Diocese of Minnesota nominated a partnered lesbian as bishop on Saturday. The Rev. Bonnie Perry is rector of All Saints Episcopal Church in Chicago and an adjunct professor at Seabury-Western Theological Seminary in Evanston, Ill. Her longtime partner is a priest in the church, according to the Times.