Kyl speaks in a formal, reserved manner that is a sharp contrast to Trump, and he belongs to an older, less populist vanguard of the GOP.
The Republican Ducey says he hopes that Kyl will serve longer.
Former Arizona Sen. Jon Kyl is well-respected in Arizona and has been able to avoid numerous battles with activists that complicated the late John McCain's career and that of the state's other senator, Jeff Flake. Their side-by-side service will be short-lived: Flake himself is retiring at the end of this Congress.
In a story published Wednesday, Woods told the paper he'd discussed the idea with Senate Minority Leader Chuck Schumer of NY and other Democratic senators.
Another unknown is whether Ducey will even be governor next year.
Before then, Democrats are hoping to pick up an Arizona Senate seat in November's election.
The Republican Kyl served previously as one of Arizona's two senators, alongside McCain. By state law, Ducey's pick had to be from McCain's party.
The choice will also have political consequences for Ducey. "He understands how the Senate functions, and will make an immediate and positive impact benefiting all Arizonans", Governor Doug Ducey said in a release.
GOP donor Dan Eberhart, who lives in Arizona, wrote in an email that Kyl was a "safe choice" for Ducey.
For now, Kyl will pad Republicans' margin in the narrowly divided Senate.
In remarks last week at a memorial service for McCain at the Arizona State Capitol, Kyl also made what many interpreted as a swipe at Trump's overly friendly relationship with Russian President Vladimir Putin. "But everyone who will [should] look at his history".
Kyl, a Republican who retired from the Senate in 2012 to spend more time with his family, is now shepherding Trump's nomination of Brett Kavanaugh to the US Supreme Court.
A spokesman for the Arizona governor says Jon Kyl could be sworn in as a USA senator as soon as Tuesday evening but it will likely occur Wednesday.
Kyl, 76, served with McCain in the Senate and rose to the position of Republican whip, the second-highest leadership post in his party's Senate leadership before retiring in 2013.
Kyl, a lobbyist, dismissed the idea that his work will impede his ability to serve in the Senate. He and his wife Caryll have two children, Kristine Kyl Gavin and John Kyl, and four grandchildren. He's undoubtedly making far more money than a senator's salary. He wouldn't speculate if he would replace Kyl should he depart after this year. Still, he said he was honored to be supporting Kavanaugh's nomination.
What about re-election in 2020?
Jon Kyl was sworn in as a replacement for Senator John McCain today by VP Mike Pence. He has said he won't run for re-election.
Graham's name was floated as a potential Senate contender in 2018, and he didn't rule out a run on Tuesday.