Cinven submitted its final binding offer to acquire Telekom Slovenije at the end of May and is in talks with the European Bank of Reconstruction and Development to join in the investment, according to a statement.
The offer, set to expire 10 June 2015, is at a 60 percent premium to the valuation that the Slovak government sold the company at last month, the firm's statement said. Reuters reported that the new offer is €130 per share, giving the company a valuation of about €850 million.
A Cinven spokesperson was not immediately available to comment.
The EBRD would be providing debt and/or equity for the transaction, according to the bank's statement.
Cinven has invested in European telecom businesses in the past, including Numericable and Ziggo.
Telekom Slovenije, founded in 1995 and based in Ljubljana, is the biggest state-owned company that was privatised, according to the statement from the EBRD, and had more than 1.15 million mobile connections at the end of the fourth quarter last year.
The EBRD was established in 1992 to support economic development in central and eastern Europe, and the institution is owned by 64 countries, the European Union and the European Investment Bank.
London-based Cinven is a buyout firm whose funds focus on Europe-based companies with an equity valuation of €300 million or more, and has €19.18 billion ($21.57 billion; £14.05 billion) in assets under management, according to PEI's Research & Analytics division. Its most recent fund, The Fifth Cinven Fund of 2012, closed on €5.3 billion, beating its €5 billion target.