The UK-based car insurer plans to float half of the company to raise around £500m.
The report said that no firm decision had been made at that time.
UK mid-market firm Penta Capital holds a 45 per cent stake in Esure via Tosca Penta Investments.
Esure is the fifth largest motor insurer in the UK with over 1.6m motor and home policyholders. It was established in 2000 by Peter Wood, founder of insurance group Direct Line, in a joint venture with UK bank Halifax.
In February 2010 Penta backed Wood and his team to complete the MBO of Esure from Lloyds Banking Group.
Tosca Penta Investments, a new single deal fund managed by Penta Capital, invested £190m in the all equity transaction.
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