Yet it was not immediately known how soon Thibodeau will make a decision on the Hornets' offer, with the Celtics heading to Orlando for Wednesday's Game 5 against the Magic and with at least two teams -- Chicago and New Jersey -- also considering Boston's defensive guru for their coaching vacancies.
Hornets general manager Jeff Bower issued a statement late Tuesday denying that the team has made a formal offer to any candidate, saying that "we will issue an official update when we have concluded the process and have reached an agreement."
The Associated Press reported Monday that the Hornets were preparing an offer for Thibodeau.
Sources say Thibodeau is eager to land his first head-coaching job and has strong support from Bower, who is close with Jeff Van Gundy, one of Thibodeau's coaching mentors.
But one source close to the situation told ESPN.com that the Hornets -- after New Orleans native Avery Johnson emerged as the early favorite for the job -- are prepared to turn to Portland Trail Blazers assistant coach Monty Williams if Thibodeau declines.
After Bower replaced Byron Scott just nine games into the season and posted a 34-39 record as interim coach, New Orleans interviewed five other candidates in addition to Thibodeau, Williams and Johnson. Dallas Mavericks assistant Dwane Casey, Utah assistant Tyrone Corbin, ex-New Jersey coach Lawrence Frank, TNT analyst and former NBA coach Mike Fratello and ESPN analyst and former All-Star guard Mark Jackson also spoke to New Orleans.
Johnson, who has been working as an analyst for ESPN since leaving the Mavericks following the 2007-08 season, is a New Orleans native and was widely considered to be the top choice of incoming Hornets owner Gary Chouest, another New Orleans native.
Johnson, though, has instead emerged as one of two finalists for the Atlanta Hawks' vacancy along with Casey, while New Orleans shifted its focus to Thibodeau and Williams.
The Hawks interviewed Johnson twice last week -- including a lengthy meeting with the team's ownership group Friday -- and have scheduled Casey for a second interview in Atlanta this week.
Sources say the Bulls, meanwhile, have scheduled an interview this week with Frank while waiting to see whether Thibodeau takes the New Orleans job or consents to meet with them after Boston's series with Orlando. Other Bulls candidates besides Frank and Thibodeau, according to the Chicago Tribune, are Houston Rockets assistant coach Elston Turner and Oklahoma City Thunder assistant coach Maurice Cheeks.
Thibodeau began his NBA coaching career as an assistant with Minnesota in 1989. He later worked as an advance scout with the Seattle SuperSonics before returning to the bench as an assistant with San Antonio, Philadelphia, New York, Houston and now the Celtics.
Considered for various head coaching jobs in recent years, Thibodeau appears to be in greater demand than ever before thanks to the smothering defense Boston has played in eliminating LeBron James' Cleveland Cavaliers in the second round and taking a 3-1 lead over Orlando in the Eastern Conference finals.
Marc Stein is a senior NBA writer for ESPN.com. Information from The Associated Press was used in this report.