Source: Sharecast
The former Treasury minister and Goldman Sachs partner has served as chair since 2016.
But according to Sky News, the west London hub has now hired recruitment firm Russell Reynolds Associates to lead the search for his replacement.
Heathrow has yet to comment on the report.
Deighton’s tenure was due to come to an end on 30 April. But writing in the annual report, published earlier this year, Deighton - who was made a peer in 2012 - said he had been asked to stay on for a "limited period to help ensure a smooth transition" while new directors became familiar with the business and a new chair was appointed.
He continued: "I have therefore agreed to extend my role as chair for a limited period to ensure continuity and stability on the board during this period of transition."
Heathrow is owned by a number of funds, including French private equity group Ardian, its biggest shareholder.
Ardian agreed to buy out three other shareholders in February, taking its stake up to 32.6%.
It followed a major shake-up in the airport’s ownership structure in December, which also saw Saudi Arabia’s sovereign wealth fund buy a stake.
Spain’s Ferrovial exited the group after 17 years following the Ardian deal - thought to be worth £870m - in February.
Under chief executive Thomas Woldbye, who was appointed in 2023, Heathrow has started pushing for a major expansion, including a long-anticipated third runway.
A formal planning application is expected to be put before parliament in 2029.