According to reports in Spanish newspaper El Pais and on the Reuters website, the deal is part of a partial sale of the world's largest airports operator.
It will see Corporación Financiera Alba take an 8% stake while Ferrovial and TCI will each take a 6.5% stake, and all will hold one seat on the 15-member board.
Spain also plans a public share offering for another 28% in Aena, meaning eventually a 49% stake will end up privately owned and it values the operator at up to €5 billion.
In July, Aena appointed the banks Santander, BBVA, Bank of America Merrill Lynch, Goldman Sachs and Morgan Stanley to run a process to sell just under half the company.
As previously reported by Airport World, in July, the aim of the saleis to make the company more efficient and attract more tourist flights, and the sale is expected to net about €2.2 billion ($2.97 billion), while the company's debt is about €11.5 billion.
Aena owns 46 airports in Spain and also has international interests, such as a stake in London's Luton Airport, but just 13 of them were profitable in 2013, including Madrid, Barcelona and tourist destinations such as Palma de Mallorca, Ibiza and Tenerife.
The gateway operator made a profit of €597 million in 2013, after huge cost reductions, including staff cuts and benefiting from airport tax increases, up from a €215 million loss in 2011.
Aena is the biggest airport operator in the world in terms of passengers, and handled more than 187.4 million travellers last year.