Muir, named chair of the approximately 200-student School of Architecture in June 2009, did not reply to phone messages or emails seeking comment.
"The school has a lot of problems and we need to work together and fix them," said Scheer, who leads the College of Architecture + Planning. "I think it's really hard for [students] to understand because they don't know what's going on."
In an email to students Tuesday, Scheer said she offered Muir three options: Stay through the remaining two years of his term and "work closely with the faculty and with me" to resolve governance and communications issues; leave June 30, or when a new chair is found; or leave now, and Scheer would ask for nominations for interim chair.
Scheer said she will set up a meeting with administrators air problems with faculty and students.
Students submitted a petition Monday seeking an investigation. Members of the faculty voted unanimously last week to express their support for Muir, said professor Patrick Tripeny, the previous chair. Tripeny served for less than three years and said Tuesday his departure from the leadership post was "not by choice."
The accreditation board hasn't issued a full report, but evaluators expressed concerns with governance and communication during a visit about two weeks ago, he said.
"They were very vague" about the governance issues, Tripeny said. Evaluators also raised a handful of other points, such as an insufficient number of emergency exits on student projects, he said.
Farnsworth, who also spoke with the evaluators, said they seemed focused primarily focused on curriculum, communication between students and administrators and studio culture. "There were 64 points the board was interested in, and we didn't pass on nine of them," he said.
Scheer declined to specify her concerns, but said she offered to work with Muir under a specific set of expectations for improvement.
Muir designed several iconic buildings along the Wasatch Front, including the Rose Wagner Performing Arts Center, the Ethel Wattis Kimball Visual Arts Center in Ogden and the Utah Museum of Fine Arts at the U.
The resignation would not change Muir's position as a professor position. "His term has been a success. He's done very many successful things," Scheer said.
Michael Hardman, interim senior vice president for academic affairs, received the students' petition with about 135 signatures and is "reviewing this issue with [Scheer]," said university spokesman Keith Sterling. It reads: "We, the undersigned students, respectfully request an investigation into the appropriateness of his termination with the hope of his reinstatement."
Kathleen Hill, who served on the Salt Lake City Planning Commission with Muir and is also an architecture graduate student, called him an "admired and respected pillar" in the architecture school and community at large.
"To tarnish his reputation so unjustly and put his performance in question is inexcusable," she said in a statement.
Graduate student Jane Collette said Muir had been trying to raise the school's profile and grow its scholarship base.
"The faculty and students are very upset," Collette said. "He's a man of real integrity."