According to Reuters, the company, which is being advised by Swiss bank UBS, could generate approximately €1.3 billion.
The mobile operator has attracted interest from private equity groups due to a relatively quiet year of mergers and acquisitions, largely caused by a weak economic climate.
Private equity firms including Apax, Bain Capital, BC Partners, EQT and Providence have all made it through, and are expected to put forward second round bids by July 5.
The successful bidders will have access to a financing package, put together by UBS, to generate confidence in the deal.
DNA is presently controlled and owned by a range of companies that were formerly local phone carriers in Finland, and its largest shareholder is Finda Group, which owns a 33% stake.
