MILAN, April 26 (Reuters) - Italy's SECO said on Monday Telecom Italia unit Olivetti bought 7.5 million shares in its initial public offering (IPO), equal to 7% of the high-tech company's final capital, which could lead to an industrial partnership.

Tuscany-based SECO, which develops embedded microcomputers and 'internet of things' solutions, is selling up to 37.8 million shares, in an offer which will run until April 30.

Just a few hours after book building kicked off, the bookrunner said that the offer was covered on the base deal size.

SECO is expected to start trading on the Milan Stock Exchange on May 5, the IPO bookrunners said in a term sheet to investors.

SECO had set the price range for its IPO in Milan at between 3.30-4.15 euros per share, aiming for a market capitalisation of up to 445 million euros ($538.36 million).

"SECO has decided to allocate the order in order to start a dialogue with Olivetti, with the aim of building an industrial partnership," SECO said in a statement.

The collaboration will be focused on the development of hardware and software technologies and proprietary internet of things solutions, the company added.

Once a well-known typewriter and computer company, Olivetti is now 100% controlled by telecoms group Telecom Italia and focuses on big data, the internet of things and retail payment instruments.

Goldman Sachs and Mediobanca are acting as joint global coordinators for the IPO. ($1 = 0.8266 euros) (Reporting by Giulia Segreti and Elisa Anzolin, editing by Louise Heavens, Kirsten Donovan)