Agency spokesman Tom Vinger tells the San Antonio Express-News that an informant told sheriff's officials that Fiala offered him $5,000 to kill the teen.
The teen filed a lawsuit in April alleging he was sexually assaulted by Fiala in 2007 and 2008.
in September the priest was arrested and indicted on three counts of aggravated sexual assault of a child and one count of aggravated sexual assault by threat. He was freed on bond.
The teen says the abuse took place during private catechism classes and in a hotel room.
The lawsuit also claims archdioceses covered up Fiala's record of abuse.
The Omaha, Nebraska archdiocese has since revealed that in 2002 a minor came forward to report a sexual assault by Fiala in the mid-1980s, according to the Express-News.
'Fiala had threatened him with physical violence and threatened to kill him before, and he was very afraid of that,' the teen's attorney Tom Rhodes said.
'My client wasn't happy that Fiala was trying to recruit someone to kill him, but he's happy Fiala is in jail now.'
Jail records show Fiala now faces a count of murder solicitation.
Bail is set at $700,000