The tactic is intended to safeguard their membership in the worldwide Anglican Communion, The Washington Times reported.
Citing e-mails sent to their dioceses by two Episcopal bishops, the newspaper said church leaders are considering "repentance" for the 2003 consecration of openly gay New Hampshire Bishop V. Gene Robinson.
In the e-mails, Arizona Bishop Kirk S. Smith and Rio Grande, Texas, Bishop Jeffrey Steenson described a March 17-22 summit of Episcopal bishops in western North Carolina, the Times reported.
"Very considerable caution" will be used in electing more homosexual bishops, Bishop Smith said, "until a wider consensus emerges." Bishop Smith is identified with the church's liberal wing, the newspaper said, while Bishop Steenson is a conservative.
Twenty-two Anglican provinces have to some degree severed relations with the Episcopal Church over its consecration of Bishop Robinson in 2003.
The 2.2-million-member Episcopal Church has expressed "regret" for the consecration, but its legal standing as the U.S. representative of worldwide Anglicanism is in jeopardy, the Times said.