The report Tuesday cited three people close to Brewer as saying she will veto SB 1062, which would allow businesses to discriminate based on grounds of religious objection.
Brewer, a Republican, has come under growing pressure to veto the bill from both of Arizona's Republican U.S. senators and three Republican state lawmakers who voted for the bill but now urge a veto. Former Massachusetts Gov. Mitt Romney, the GOP 2012 presidential nominee, joined the opposition Tuesday, posting a Twitter message telling Brewer "veto of SB 1062 is right."
Chuck Coughlin, a longtime Brewer political adviser, told NBC News the governor has tended to "focus on the priorities she wants them [the Legislature] to accomplish, and this was clearly not part of her agenda."
Arizona business interests have urged a veto, some saying even the prospect the bill might become law is already causing the state to lose business.
"She doesn't want to take any actions that could jeopardize the economic momentum we've seen here in Arizona," someone close to Brewer told NBC.
Coughlin said Brewer, who was returning to Arizona Tuesday after the National Governors Association meeting in Washington, planned to meet Wednesday with opponents and backers of SB 1062 and would probably reach a decision Thursday or Friday.
Hundreds of protesters gathered in front of the Capitol Monday.
A sign carried by Rabbi John Linder read: "Governor Brewer, I'm a Rabbi, I'm a Straight Man, I'm a Human Being. Please, Veto SB 1062."
Linder said it was important for him "to be a model for the kind of compassionate congregation that we are creating and to send a message to the interfaith community that we are joined here today."
Al Gephart, a Presbyterian minister with a transgender daughter, said: "Christianity at its center is not exclusive. It's inclusive."
Signing the bill would represent a step back for civil rights, fellow parishioner Laura Green said.
"If we allow this," she said, "then what's next?"
Another protester, Adam Leeds-Peralta, said the bill would legalize discrimination against gays.