Aena, the Spanish airport operator, already holds 10% in the gateway, which Abertis is shedding as the final piece of its TBI airports division.
Negotiations are in "the final stages", an Aena spokesperson told the UK's Financial Times last week.
The newspaper said a deal could be announced as early as today, according to "people close to the talks".
While Aena controls 47 airports in Spain, Luton would be the company’s first non-Spanish airport.
Aena has announced a goal of raising capacity at Luton to 18 million, up from 10 million in 2012.
London Luton appeals to Aena as high-season flights from the gateway connect to 14 Spanish airports run by the operator, according to the Financial Times.
Last week, Abertis announced it had agreed the sale of Belfast International and Stockholm Skavsta airports, as well as Orlando Sanford (Florida) airport terminal concessions and TBI's airport management business in the US.
In March, the company agreed to sell Cardiff Airport to the Government of Wales.
Abertis gained these gateway through its purchase, with Aena Internacional, of the British operator TBI in 2005.
An Abertis spokesperson confirmed to Airport World that the firm is in talks with Aena over Luton Airport but gave no comment on when an agreement is expected.