Veteran Jesse Kelly will officially announce his candidacy to run for the Republican nomination in the special election. He narrowly lost to Giffords in her 2010 re-election bid.
Gov. Jan Brewer (R) will have until 5 p.m. Saturday to call a special election and to set the primary special date. She legally has an additional seven days to set the general special election date, but Brewer is expected to set both dates by Saturday.
The primary will occur 80 to 90 days after the vacancy, and the general will occur 50 to 60 days after the primary.
Other Republicans mentioned as possible candidates are state Sen. Frank Antenori and college sports TV broadcaster Dave Sitton.
Names being discussed on the Democratic side include state Sen. Linda Lopez of Tucson, who is close to Giffords; state Senate Minority Whip Paula Aboud; state Rep. Steve Farley; Pima County Supervisor Ramon Valadez; and businesswoman Nan Stockholm Walden.
“Her service will be deeply missed, and I join the people of Arizona in praying for her continued recovery,” Brewer said in a statement about Giffords.