More than 8000 jobs are at risk across the UK.
Zolfo Cooper, which has been appointed as administrator, said it was "likely a number of stores would need to be closed to make the business financially viable".
The group, which operates 628 Clinton and 139 Birthdays stores, had made losses of £130million since 2004.
Clinton has Glasgow stores in Sauchiehall Street, Argyle Street, Byres Road and Crown Road, in Partick.
It also has shops in the Buchanan Galleries, the St Enoch Centre, Silverburn shopping centre, The Fort in Easterhouse, and Braehead shopping centre.
It also operates stores in Paisley, Newton Mearns, East Kilbride, Kilmarnock, Greenock, Airdrie, Clydebank, Coatbridge, Bellshill, Motherwell and Hamilton.
It is not yet known how many jobs are at risk.