The investment house, which is headed up by the French business woman Dominique Senequier, also has a 49 per cent stake in Italian airport network 2i Aeroporti, and has interests in Milan's Malpensa and Linate airports.
Ardian first approached Ferrovial about buying its Heathrow stake last year, Reuters reported, but discussions did not advance.
It is understood that any current discussions over Ferrovial's interest may not result in a sale.
Ferrovial has previously warned that it would be sceptical about committing further funding to Heathrow if the airport cannot win an appropriate increase in airport charges from regulators.
Ignacio Madridejos, Ferrovial's chief executive, said in 2020 that it could "rotate the asset" if "regulation is at a level that we cannot get an adequate return for our investors".
Heathrow, meanwhile, has said it needs to raise the fees to make sure the airport does not fall into disrepair.
The CAA said in June that the cap on landing fees charged per passenger at Heathrow will fall from £30.19 to £26.31 by 2026, despite a furious lobbying effort by the airport to raise charges to more than £40.
John Holland-Kaye, chief executive of Heathrow, hit out at the decision, adding that it underestimated "the fair investment needed" for maintaining operations at the airport.
He said: "Uncorrected, these elements of the CAA's proposal will only result in passengers getting a worse experience at Heathrow as investment in service dries up.
"The CAA's proposal will undermine the delivery of key improvements for passengers, while also raising serious questions about Britain's attractiveness to private investors."
An airport industry source said the lower charges "will not allow investment" into Heathrow and would not "incentivise" shareholders to provide further funding to Britain's leading travel hub.
They confirmed that the row over charges would be a key factor in any discussions over a sale of Ferrovial's stake.
The CAA is currently consulting on airport charges and is expected to reach a decision in the autumn.
Ignacio Castejon, Ferrovial's airport head, warned last year that the Spaniards had reservations about providing more investment to Heathrow in light of the CAA's proposals.
He said: "[It] makes me feel very sceptical about the appetite to contribute further capital into Heathrow."
Experts have also warned that any decision to cut off funding was likely to scupper plans for a third runway at Heathrow, with progress already disrupted by a sharp fall in air travel during the pandemic.
It comes amid continued chaos in Heathrow's terminals after it struggled to find enough staff to meet demand for a return to air travel after the pandemic.
Heathrow was recently forced to impose limits on inbound and outbound flights due to staff shortages, in a move that could trigger more flight cancellations.
The airport asked carriers to stop selling tickets for summer holidays and imposed a departure limit of 100,000 passengers per day.
The west London airport told carriers it could limit flights until at least October 29 and threatened to sue airlines that failed to reduce capacity.
Mark Powell, Heathrow's director of operational planning, warned that the airport was introducing "contingency" measures to avert "dangerous" overgrounding in terminals.
The airport has reported a £321m (NZ$617m) loss for the first six months of the year as it struggled with the return of travellers after pandemic restrictions eased.
It blamed a lack of ground handling staff for its issues and estimated there had been a 30 per cent decline in staffing levels since the pandemic.
Madrid-based Ferrorival also controls Spanish infrastructure developer Cintra and has been invested in Heathrow airport for 16 years. It purchased an indirect stake of almost 56 per cent in Heathrow in 2006 and eventually reduced its stake to 25 per cent in 2013.
Ferrovial is Heathrow's largest investor and sits alongside the Qatar Investment Authority, which holds a 20 per cent stake, as well as Caisse de dépôt et placement du Québec, Singapore's wealth fund GIC and China Investment Corporation.
-By Helen Cahill
