Leahy, who turned 65 in August, has told colleagues he will stay in one of aerospace's most visible and highest-paid jobs for a "few more years", they said.
An Airbus spokesman said it did not comment on rumours about individual executives.
Leahy said in June he was thinking about whether to retire after more than two decades as top Airbus salesman, during which it rose to equal and, until recently, surpass U.S. rival Boeing as the world's largest planemaker.
"I am 65 and I do have to decide whether I have to retire or not, but one has to worry about one's health and what you do for a living too," he told a news conference.
He was speaking after closing the Paris Airshow with a trademark deal to sell 110 planes to Hungary's Wizzair, accelerating negotiations to win the premier event rather than risk a rare defeat to Boeing on home soil.
The all-night negotiations demonstrated a winner-takes-all approach that has significantly boosted Airbus's market share and secured thousands of European jobs, but which has raised sporadic concerns among analysts over pricing and margins.
Both Airbus and Boeing have accused each other of starting price wars during Leahy's tenure.
Leahy joined Airbus in 1985 and made a reputation for cutting innovative "walkaway" deals to boost its market share from 18 percent, when he became sales chief in 1994, to around 50 percent.
The New Yorker has outlasted half a dozen Airbus CEOs and numerous Boeing counterparts, but recently Airbus CEO Fabrice Bregier has taken a bigger profile in international successes.
The replacement of such a key figure would be a watershed moment for Airbus, which has fallen back to second place in terms of deliveries against Boeing but continues to outsell it.
Bregier appeared to give Leahy free rein at the June news conference, telling him "you will retire within 15 years".
Leahy is one of the industry's best-known figures but also a polarising one whose taped speeches are used to fire up opponents.
His constant jabs at "my friends in Seattle" are fiercely resented by many Boeing executives, who have hit back with a more aggressive approach and a series of major wins under Boeing Commercial Airplanes CEO Ray Conner in recent years.
Leahy's decision to remain guarantees more competition, but critics say Airbus may be storing up longer-term difficulties by relying too much on his hard-charging style.
"The longer he stays, the harder it will be for them when he leaves," an industry source said, asking not to be named.
(Reporting by Tim Hepher; editing by Susan Thomas)
By Tim Hepher