Airport operator BAA has said it is to cut jobs, but has played down reports that 2,000 positions may go.
There have been calls for BAA to be split up
BAA said some jobs would be lost, but it did not yet have a final number, adding that security and customer service roles would be unaffected.
The positions are being removed as part of an efficiency review at the UK's largest airport business.
BAA owns Heathrow, Gatwick, Stansted, Edinburgh, Glasgow, Aberdeen and Southampton airports.
The company denied reports that it was also looking at selling one or more of its sites.
Unions criticised the planned job cuts as illogical but one leading airline said it would support the move as long as it did not affect security or passenger services.
The Times newspaper had reported that the airport operator was to cut 2,000 jobs, but a spokeswoman for the company said BAA did "not recognise" that figure.
"This is a simplification exercise aimed at support staff much more than frontline staff," said BAA.
"It's not simply about costs. It's about building a much leaner and more efficient business."
Standards at Heathrow have come under fire from airlines, ministers and key business figures as well as London mayor Ken Livingstone.
Unions said the airport's problems were partly due to a lack of trained staff and any future cuts would make conditions even more difficult.
"It would turn logic on its head if the company were to seek to resolve its difficulties through slashing jobs in a bid to maximise short-term profits," said Brendan Gold, national secretary for Unite.
"We would, of course, strongly resist any compulsory redundancies."
Virgin Atlantic, one of the BAA's largest customers, said the airports operator had been overstaffed for some time.
But it warned that job cuts must not threaten security procedures or inconvenience passengers.
These comments were echoed by British Airways which said BAA should become "more efficient" in how it operated but did not want any cuts to affect frontline services.
BAA has a 60% market share of all UK passenger flights, rising to 90% in the south of England.
The firm, which was bought by Spanish firm Ferrovial last year, is at the centre of a Competition Commission probe into whether it excessively dominates the market.
BAA's level of customer service is expected to feature in the commission's investigation.
The firm has previously accepted that "the experience of too many passengers using London airports is unsatisfactory", but blames a lack of capacity in terminals and on runways.