Whether or not Kaine wins the vice presidency next week, his term is up in 2018. But if he has to resign, there will also be a special election in 2017, and Fiorina, who resides just south of Washington, D.C. in Mason Neck, Va., is considering entering the race — but won’t make a decision on whether to do so until after Election Day, sources with knowledge of her thinking say.

Republicans in the state are urging Fiorina to run because she would bring immediate star power and fundraising ability to the expensive, back-to-back races for Kaine’s seat that will take place if he becomes vice president. Fiorina is not the only Republican interested, and the GOP field could end up being large. But her national name recognition after the 2016 presidential campaign would make Fiorina particularly formidable in a GOP primary.

“It’s something she’s taking a very strong look at,” a Virginia GOP operative said. “She’s not just name ID, she’s got serious definition. People have seen her, they know what she can do.”

Fiorina has traversed Virginia helping down-ballot candidates this fall, in addition to her continued engagement in national politics since her presidential run.