Business information and events group UBM, US buyout firm GTCR and German media analysis business Unicepta are also tipped to have their eye on the firm, said the Sunday Telegraph.
Gorkana was founded in 2005. The company provides data about jobs and contact details for people working in PR and journalism. It also has a press cuttings arm and a social media monitoring division.
Exponent is reportedly aiming to raise around £200m (€253.3m) for the business.
DC Advisory is said to be advising Exponent on the Gorkana sale with the first round bids due by September 10.
3i declined to comment on the deal.
Exponent introduced John Moore as executive chairman at Gorkana in 2007 and bought fully into the company in 2010.
Earlier this year Exponent was reportedly interviewing banks to manage the sale of aircraft replacement parts distributor Pattonair, for more than $500m.
The company is still listed in the firm’s current portfolio on its website.
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