Arizona Gov. Doug Ducey bid farewell to chief of staff Kirk Adams on Monday, sparking speculation that the Republican's departing top aide could end up in the U.S. Senate that used to belong to the late Sen. John McCain.

Ducey, freshly re-elected, could soon appoint a successor to Sen. Jon Kyl, the Republican he appointed in late August to replace McCain on an interim basis. Adams, Republican insiders told the Washington Examiner, could end up on Ducey's shortlist. So too could Rep. Martha McSally, the Republican congresswoman who lost a hard fought race for the Senate seat being vacated by Sen. Jeff Flake, R-Ariz. Rep. Kyrsten Sinema, a Democrat, won that race.

Kyl, a former elected senator, agreed to serve again as a caretaker to get the GOP through a politically delicate period in the run-up to the midterm elections. He could resign his appointment soon.

In the meantime, Ducey is facing pressure from Republicans to appoint someone who would run in a 2020 special election to determine control of the seat for the final two years of the term McCain won in 2016.

Other names being mentioned include former Rep. Matt Salmon, a Republican and a conservative stalwart; state Treasurer Eileen Klein; and Maricopa County District Attorney Bill Montgomery. The county is comprised of Phoenix and surrounding suburbs, a key driver in Arizona elections.