Barbara Anthony, the state’s undersecretary for consumer affairs since 2009, is “very seriously considering running for attorney general,” a person familiar with Anthony’s thinking said today, as the fallout begins over Attorney General Martha Coakley’s decision to run for governor.

Anthony, who was appointed by Governor Deval Patrick, has consulted strategists about running for the state’s top law enforcement post, the person said.

“I know she’s very close to a final decision,” said the person, who asked not to be quoted so as not to violate private conversations.

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According to the state’s consumer affairs website, Anthony was executive director of Health Law Advocates, a non-profit law firm, and Northeast director of the Federal Trade Commission. She has also worked as chief of the state attorney general office’s public protection bureau and as chief compliance officer of Bay Banks.

The decision by Coakley, who launched a campaign tour Monday morning, to run for the corner office has continued shaking loose the state’s political infrastructure. Secretary of State William F. Galvin is considered a prospective candidate for attorney general.