Spanish newspaper Expansion said the offer, for which Ferrovial is reported to have held talks over a joint bid with at least two Australian funds Macquarie and Industry Funds Management, was worth $1.3 billion (£800 million).
The move comes at a time when business is booming for the two Scottish airports after they, like other airports, suffered from falling passenger numbers during the financial crisis.
More than 3.48 million people passed through Aberdeen International Airport in 2013, taking it above the previous record of 3.43 million in 2007 before the economic downturn.
Meanwhile Glasgow airport had its busiest year since 2008 after 7.4 million passengers travelled via its halls in 2013.
The potential move comes at a time of great change in the Scottish airport sector.
In November Prestwick Airport in Ayrshire was bought by the Scottish Government for £1.
The facility, which was put up for sale in 2012 by New Zealand firm Infratil, had been incurring annual losses of £2m with just one million passengers using it every year.
In 2012 Heathrow sold Edinburgh Airport, which sees nine million passengers a year, to Global Infrastructure Partners, owner of Gatwick Airport.
Ferrovial bought Heathrow and a number of other UK airports as part of its acquisition of BAA in 2006 for £10.3bn.
As the credit crunch hit making large debt piles unattractive, it gradually sold stakes to new partners at a profit to reduce debt. It now has a 25% interest in HAH.
The sale of Edinburgh airport followed a competition ruling that also forced it to divest Gatwick and Stansted airports, near London.
Ferrovial is now seemingly keen to diversify away from its domestic construction business, which has been hit by the economic crisis in Spain. But its partners in the HAH consortium, Britannia Airport Partners, Singapore's GIC, Qatar Holding and Alinda Capital Partners, prefer to focus on Heathrow, Britain's busiest airport, and sell the other airports.
Some estimates suggest that Heathrow provides between 80% and 90% of the group's business.
HAH, Ferrovial, Glasgow Airport and Aberdeen Airport all declined to comment.
The rebound of the Scottish airports from the economic downturn has continued into 2014.
More than 436,000 passengers travelled through Glasgow Airport last month, up 6% on the same period last year.
The airport said domestic traffic grew by 4%, benefiting from strong demand for Glasgow's London routes, while international traffic grew by 9%.
Meanwhile, almost 251,400 people passed through Aberdeen Airport last month, a rise of 9.8% on January 2013. Helicopter passenger numbers were up 17.8% and those for fixed-wing aircraft were up 8.5%.
January is typically a quiet month for Scotland's airports.
Meanwhile, heated debates continue about the future of the London airports.
In December Sir Howard Davies delivered the Airports Commission's interim report to the Government about the future of London aviation.
It had an effective shortlist of two options for Heathrow Airport, either an expanded existing runway or a new one, or a new runway for Gatwick, by 2030.
Ferrovial has other involvement with Scottish infrastructure.
It is part of the Scot Roads Partnership which is the Scottish Government's preferred contractor for works due to take place on the M8 between Glasgow and Edinburgh and the connected M73 and M74.
Last year Ferrovial bought Enterprise, a UK business services company, for £385m.
A £17m refurbishment of Glasgow Airport is currently being undertaken ahead of the Commonwealth Games this summer.