The union said management was allowing "only" two weeks for staff, industry and the local community to provide feedback on the centre's closure, which it slammed as not being long enough.
Barker said it was no longer sustainable for the university to keep subsidising the centre.
"The Centre has struggled to attract enough students to become economically viable, and the prospect of growth of student numbers to a feasible level in the short to medium term is unlikely.
"Also, the centre's income is substantially less than its cost, and consequently there is in an annual deficit of several hundred thousand dollars.
"This deficit is currently being paid by subsidies from other areas of the university.
"Additionally, sustaining the Centre's infrastructure requires significant investment," Barker said.
The proposal has been analysed for some time and before the formal consultation started Barker said he and the centre had been involved in a long period of informal consultation.
Under the proposal four FTE permanent academic and one FTE permanent general staff positions would be disestablished.
"Dependent on the outcome of consultation of the proposal I am hopeful that several staff will be in a position to take advantage of other opportunities within the University.
"For example, some staff could be transferred to the Department of Food Science."
Barker said he recognised that this is a stressful time for staff and support is being offered. He had also contacted students.
"If the proposal goes ahead, it is my intention to offer an unchanged programme to existing students for 2018 and hopefully into 2019."
A final decision on the proposal was anticipated in mid-December.
Otago University TEU branch organiser Kris Smith said the loss of the centre would be a "disaster".
"No longer would future generations with an interest in the science and cultural impact of fibres, textiles and clothing look to the University of Otago as the path towards a fulfilling career in a wide range of sectors.
"New Zealand would also lose research capabilities in these hugely important fields.
"Management cannot possibly expect to speak to all affected stakeholders in the two weeks it is allowing for feedback.
"They would be wise to extend the consultation period to allow enough time for staff and industry to get around the table to work out a plan for the Centre's future.
"Perhaps then management will hear just how important these qualifications are to New Zealand."