However, Xavier athletic director Mike Bobinski told the Cincinnati Enquirer on Sunday that the Musketeers were prepared to make a counteroffer -- if necessary.
A source said Miller took a private plane Sunday morning en route to Albuquerque, where he met with Livengood about the Wildcats' opening.
On Saturday, Bobinski told ESPN.com he wasn't sure Miller would talk to Arizona and he had not heard from Arizona as of Saturday. On Sunday, Bobinski told the Enquirer that Miller had kept him up to date as the situation developed.
"People's feelings and thoughts changed," Bobinski told the Enquirer. "You would not be incorrect in assuming that's what happened here. Searches are fluid processes and things change, but Sean has been great in letting me know what's going on.
"We have done and will continue to do whatever is humanely possible to keep Sean."
Bobinski told ESPN.com Sunday night that he expected to speak with Miller late Sunday or early Monday. In a text to ESPN.com, he wrote: "Nothing firm at this moment, but I remain very optimistic that Sean Miller will continue as our head basketball coach at Xavier."
Bobinski later said in a text that he didn't anticipate a final resolution Sunday night.
Miller "has a potential Final Four team coming back next season, loves where he lives, has security and is paid well and has the best job in his league, yet has to decide whether or not this is the right job for him to explore," Calipari said.
Arizona went down a similar path last week with USC coach Tim Floyd. He interviewed, was offered the gig but chose to remain with the Trojans. Arizona tried to pursue Gonzaga's Mark Few and Pitt's Jamie Dixon prior to interviewing Floyd.
Miller has coached five seasons at Xavier, making four consecutive NCAA tournament appearances. He reached the Sweet 16 this season and the Elite Eight in 2007-08. His contract with Xavier is through the 2015-16 season.
Arizona reached the Sweet 16 this year under interim coach Russ Pennell.
Lute Olson retired as coach after 25 years in October 2008 for health reasons. Olson missed all of the 2007-08 season after taking a personal leave of absence for what he later termed "a medical condition that was not life-threatening."
Andy Katz is a senior writer at ESPN.com. Information from The Associated Press was used in this report.