Les Miles met with Michigan on Monday evening about the Wolverines' coaching vacancy, shortly after the LSU coach said he is also "extremely happy" with his current job.
LSU spokesman Michael Bonnette confirmed that the meeting took place but could not immediately say which Michigan officials were involved.
A Domino's Pizza jet arrived in Baton Rouge on Monday afternoon and was on the ground for nearly five hours before departing for an airport near Michigan's campus. When the plane landed at Willow Run Airport, Brandon got off but did not provide any details about the search to reporters waiting at the airport.
Bonnette said Miles' status as LSU's coach remained unchanged and that he and Miles still planned to travel to Dallas on Tuesday for Miles' previously scheduled speaking engagement at an American Football Coaches Association gathering.
Earlier Monday, Miles attended LSU cornerback Patrick Peterson's announcement that he was entering the NFL draft, then spoke afterward about the direction of his coaching career.
"The only thing I can tell you is, I spent my day today with a number of underclassmen that I want to return right here," Miles said. "I am extremely happy here. There's a real comfort with my family here in Baton Rouge. I think it's best left that way and I don't know that there's anything more to say."
LSU athletic director Joe Alleva did not object to Miles meeting with Michigan but reaffirmed comments he made over the weekend concerning LSU's intention to retain its coach.
"I can certainly understand coach Miles' desire to accommodate his alma mater by speaking with them during their coaching search," Alleva said. "We remain committed to working toward keeping Les Miles as the head of the LSU football program, a program that wins at a high level, graduates its student-athletes and represents the university well in the community under his leadership."
Brandon has been very quiet about details of his search since firing Rich Rodriguez last week other than to confirm Friday he was using some "external resources" to help him find a new leader for college football's winningest program.
"Some would suggest we should complete this national search in a matter of hours," Brandon wrote in a blog post on mgoblue.com Monday. "But this is a critical decision for Michigan Athletics and it cannot and will not be made in haste."
Miles was an offensive lineman on two Big Ten championship teams for the late Bo Schembechler, who later gave Miles his first chance to be an assistant coach in 1980. Brandon is a former teammate.
Last Wednesday, Rich Rodriguez was fired as Michigan coach with a 15-22 mark in three seasons.
Miles is 62-17 with a 2007 national championship in six seasons at LSU since taking over for Nick Saban in 2005. He is coming of a 41-24 victory over Texas A&M in the Cotton Bowl that gave him his fourth season with at least 11 wins the Tigers. He also has a 5-1 record in bowl games at LSU.
Miles' LSU contract pays him $3.75 million per year, runs through 2014 and includes an annual one-year roll-over at the discretion of the athletic director that could extend the deal to 2015. The contract also would make him among the three highest paid college coaches should he win a second national title at LSU.
If Miles were to head back to Michigan, he'd be taking on a rebuilding project while also leaving behind a program that is bound to be a favorite in the mighty SEC in 2011.
Next season would be Miles' seventh at LSU, where he has brought one highly rated recruiting class after another to Baton Rouge.
In addition, Miles last month signed coveted 6-foot-5, 230-pound junior college transfer quarterback Zach Mettenberger, a former top Georgia recruit who was dismissed by the Bulldogs because of legal trouble.
Mettenberger's arrival is expected to provide a boost to LSU's passing game, which was last in the SEC this season, and was perhaps the only thing holding the Tigers back in their two losses this season to Auburn and Arkansas.
Mettenberger will compete for snaps with rising senior Jordan Jefferson, who struggled for long stretches but is coming off an impressive performance in the Cotton Bowl in which he accounted for four touchdowns.
After Peterson announced that he would enter the NFL draft, he said he hopes and believes Miles will remain at LSU, based on his conversations with the coach and what Miles has told other underclassmen and recruits.
Peterson's younger brother, Avery Johnson, is a high school junior and standout wide receiver who has made an early commitment to LSU.
"I think he's here. He said this is the greatest job in America and I believe him. He's honest with his ball players and up front with us," Peterson said. "I hope he's coming back, but he said he's here. ... So I can't wait to see the final decision and Avery will be on his way as well."
AP Sports Writer Larry Lage in Ann Arbor, Mich., contributed to this report.