In an email to Los Angeles Times political reporter Maeve Reston, Romney said he had been asked "by some friends in the local R [Republican] party to consider running and not dismiss it out of hand.
"Out of respect for them, I agreed not to rule it out until today after allowing for some discussions. It's now safe to say that I will not run for mayor."
Romney, 41, is senior vice president for capital markets at Excel Trust Inc. His residence is outside the city limits, but he could have moved; his parents own a home in La Jolla.
When Romney's name was listed by a pollster among potential candidates, it created a slight buzz within media and political circles.
Filner, a Democrat, is set to resign at 5 p.m. Friday under a cloud of sexual harassment allegations.
Republican leaders are hoping to rally around a single candidate in the Nov. 19 special election in hopes of overcoming a voter registration disadvantage. Democrats comprise 40% of registered voters within the city; voters who decline to state a party comprise 27%; and Republicans are 26%.
"Our fine city needs a good mayor and I hope that the election allows us to unite around a principled leader," Romney said in his email.
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