According to director general and CEO of the MUHC, Norman Rinfret, the human resources department received about 50 calls on Friday.
The calls came from staff members who were asking to apply to positions at other hospitals within the MUHC's network.
In December, health minister Réjean Hébert said he was considering transferring the hospital's control from the McGill University Health Centre to the local health and social services network in Lachine.
Rinfret said he is hoping Montreal's Health and Social Services Agency will soon come to a decision about the hospital's future.
"We would like this to be done extremely quickly, because we are quite concerned that people of Lachine [hospital] could decide by collective agreement to transfer to other positions [within the MUHC network]," he said.
Line Larocque is the local president of the SPSICR, a union representing nurses, nursing assistants and cardio respiratory staff.
She said staff are leaving the hospital because of uncertainty surrounding their jobs.
Yesterday, union leaders sent a letter to Quebec Health Minister Réjean Hébert, warning him that his plans could cause an exodus among staff, potentially affecting patient care.
The letter states that the union leaders were "astonished" to learn about Hébert's plans to remove the hospital from the MUHC network.
"We do not understand why you made this unilateral decision, without consulting with key stakeholders," the letter states.
Situation was 'deplorable'
When the MUHC first took over the Lachine Hospital in 2008, the hospital was in a "deplorable situation," according to Rinfret.
After investing significant time and energy into improving the hospital, Rinfret said he would prefer to keep Lachine the way it is.
Hébert has asked the Montreal Health and Social Services Agency to make recommendations on the future of the Lachine Hospital and submit them by May.