The faculty who started the petition said in an email Friday night that they are "pleased, but not surprised" that the petition received more than 50 signatures online and hard copy.
The petition requests a special meeting of University Council to discuss whether faculty still has confidence in the senior administration, and a special meeting requires a petition signed by at least 50 members of the council.
The faculty also says it will keep the petition open for several weeks while the signatures are compiled and prepared for delivery to the executive director of the University Secretariat.
The faculty claim non-academic positions have increased while teaching jobs have been cut, that education is being hurt and that donor funds are being mismanaged.
Lee Elliot, chairman of the university's board of governors said in a written statement earlier this week that the board has confidence in the school's administration.
A document accompanying the petition outlines the concerns of the faculty members.
It says: "Reduced academic resources in core faculties of the university have diminished the research profile of the university, reduced the number and range of courses we offer, reduced the quality of our programs, and thereby reduced the quality of the education we provide.''
It claims the president and academic vice-president "are responsible for a significant portion of these damages.''
The faculty members also say there are questions of transparency over how money is spent.
If the University Council passes the motion, a non-confidence vote could be held by secret ballot.
The University of Regina has been struggling to balance its budget and facing controversy involving a carbon capture centre.
The school had hoped to see an operating increase of between four and five per cent in the budget tabled by the Saskatchewan government in March. It got about two per cent.
In May, Saskatchewan's auditor told the University of Regina to fix its policies for research projects.
Bonnie Lysyk made 26 recommendations on oversight, updating policies and procedures, evaluating risks and monitoring compliance.