It is understood that the publisher, which was established in 1905 and produces more than 200m magazines and newspapers each year, plans to eliminate the day shift from production at the site.
A spokesman for the company said that the Glasgow print operation had been running at less than optimum volumes for some time.
"The company must reduce its costs if it is to be successful in the current economic climate," he added.
According to the business, which publishes titles including Dundee's The Evening Telegraph and The Sunday Post, it plans to redeploy staff into other roles in the company.
However, the publisher, which employs around 2,000 staff in total, said it is looking for voluntary redundancies. It added that compulsory redundancies "cannot be ruled out".
DC Thomson has three sites in Dundee, as well as facilities in Glasgow, Manchester and London.
Unite could not be reached for comment at the time of writing.