The 283-room hotel, near to the SECC and Glasgow Science Centre, is the largest of the 11 sites which are up for grabs.
It is currently going through a £1m refurbishment programme which will see an overhaul of all rooms, a new entrance, landscaping and improved conference and dining facilities
There are two other Crowne Plaza hotels, in Chester and Nottingham, being sold. As well as those there are seven Holiday Inns and a Best Western located in and around the midlands and south of England.
The entire portfolio has close to 2000 rooms and is operated by QMH UK.
Specialist property adviser Christie + Co has been appointed to market the hotels, which it described as being in "key trading locations".
It said: "The group has benefited from an ongoing extensive multi-million pound refurbishment programme with recent investments in key assets."
Jeremy Hill, from Christie + Co, added: "A portfolio of this standing presents an unmissable opportunity to acquire a high quality, well invested nationwide group of hotels with a profitable trading profile and a leading management team in place.
"It is a particularly attractive proposition given the growing momentum in the regional hotel marketplace."
Goldman Sachs bought hotel operator Queens Moat Houses in 2005 and renamed the business as QMH.
Christie + Co said it would not comment on a potential price for the portfolio.
Trade reports suggested it was likely to be up for sale for between £130m and £150m.
QMH UK had a pre-tax profit of £2.3m in 2012, according to its most recent accounts at Companies House.