Kirkpatrick, lost her challenge to Sen. John McCain last year, recently moved to Tucson, which is in the district, the Arizona Daily Star reported.
She said she has launched an exploratory committee and plans to tour the entire district.
However, Kirkpatrick would face a crowded Democratic primary, with eight Democrats either having announced or are considering a run.
The district was one of 23 with a Republican representative that voted for Hillary Clinton, according to an analysis by the Daily Kos.
Kirkpatrick represented the 1st District from 2009 to 2011 and again from 2013 until she opted to run against McCain.