Secretary of Education William J. Bennett may have been a candidate for the presidency of the University of Michigan--or maybe not.

A brouhaha briefly burst upon the Ann Arbor campus when Bennett's name was bandied about in regards to the vacant college presidency, but University of Michigan and government officials strongly deny he was ever seriously considered for the top job.

The controversy began when Bennett was approached by a regent of the university during a trip the secretary made to the school late last spring, said Bennett's press secretary, Loye W. Miller. At that time, the regent told Bennett he greatly admired the education secretary, and requested an appointment to speak to the secretary about the university's search for a president, Miller said.

The regent, who Miller declined to identify, met with Bennett this summer. The regent talked with the controversial secretary "in general terms" about the qualifications necessary for a good university president. The regent asked Bennett to suggest some candidates for Michigan's presidency, and Bennett sent him a list of suggestions the following week. Bennett did not place his name on that list, Miller said.

Bennett has not had any further contact with the University of Michigan concerning this matter, Miller said. "One regent does not a search committee make."

Michigan President Harold Shapiro will step down on Jan. 1 to take over the presidency of Princeton University from William G. Bowen.

The University of Michigan Board of Regents has conducted a search for a new president for the past six months.

"We have a list of about 350 names that we are considering at this point," said Regent Nellie M. Varner. "I don't recall seeing [Bennett's name] on the list, but I couldn't say for sure," Varner said that she could not comment on Bennett's chances for the post, should he be nominated. "There is a lot of research that we will have to do on all the candidates and we haven't gotten around to that at this point."

"We're trying to do a very thorough job," said Regent Neil Neilson. Neilson said he hopes to have refined the list of candidates by January but until then "anybody is a contender."

However, Neilson discounted the possibility that the university would seek Bennett to fill the presidency. "You can't believe everything you read in the Daily," he said, referring to the daily campus newspaper, which splashed rumors of Bennett's candidacy on its front page last week.

Miller also downplayed Bennett's chances as a presidential contender at Michigan. "Secretary Bennett has always been frank and candid about his views on higher education. He realizes that it is highly unlikely that any institute of higher education would seriously consider him as a president," Miller said.

Miller said that rumors about Bennett considering a university post started when Newsweek magazine learned that officials from the University of Tennessee last month had a conversation with Bennett "concerning what an institution of higher education might look for in a president."

The University of Tennessee is seeking a replacement for President Edward J. Boliag, who will step down in June. Beauchamp E. Brogan, general counsel and secretary of the board of trustees for the University of Tennessee, said that there was no foundation to rumors that the university was seeking Bennett for that post.

Boliag said that two trustees from the university met with Bennett to ask for input concerning candidates, but "they didn't ask him" if he would consider the post himself.

"The secretary frankly does not expect to hear any more from either [the University of Michigan or the University of Tennessee]," Miller said.

Bennett "does not expect to remain [education secretary] beyond the end of the Reagan Administration. He might like to do some teaching or writing," after his term in office, and might consider taking a position in a think tank or a teaching post at a university, Miller said.