The two companies, which were majority owners of ISS from 2005 until last year, will completely exit the business, which they listed on the Copenhagen stock exchange.
Goldman Sachs, UBS and Nordea Bank are running the accelerated bookbuilding. The firms also helped to bring ISS to market for its stock market float.
The banks are placing up to 35.8m shares, equivalent to about 19.3 per cent of ISS’ shares.
EQT and Goldman have been selling down their stake piece by piece since listing the group.
Last September, they sold 31m shares and in December a further 25m shares. Shares in the Danish facilities services group ended the day down four per cent. ISS yesterday reported a fall in fourth-quarter net profits.