One source close to Miles said a time and place has not been finalized. Another source said the coach would give LSU 24 hours notification before the interview and that had not occurred.
Miles, a Michigan alum, would be interested in listening to athletic director Dave Brandon, one source close to him said.
Miles has won 62 games in six seasons at LSU including the 2007 national championship.
Earlier Saturday, LSU athletic director Joe Alleva released a statement saying the school had not spoken with anyone from Michigan.
"I have not been contacted by anyone from the University of Michigan about Les Miles," Alleva said. "Les Miles is LSU's head coach and we are going to do everything we can to keep it that way. He has had great success here and we plan to keep enjoying that success under his leadership."
Miles has more than $18 million guaranteed left on his contract, a source said. If Miles were to leave for Michigan, LSU would be owed $1.25 million, with no buyout for any other school, the source said.
Michigan had a conversation with Miles when the job was open at the end of the 2007 season, though Miles said he was offering advice in the search and was not a candidate.
Miles played offensive line for Michigan and was a graduate assistant and then coach there from 1987-1994.
Harbaugh took the job as San Francisco 49ers coach on Friday. Fitzgerald said he is not interested.
San Diego State coach Brady Hoke is another potential candidate.
Joe Schad is a college football reporter for ESPN.com.