The bid has been tabled through BA's existing French subsidiary, Air Liberte.
AOM, one of the state assets formerly owned by Credit Lyonnais, has a 10-15 per cent share of the French market and is thought to be worth pounds 120m to pounds 130m.
BA faces competition for AOM from the French flag-carrier Air France, as well as Lufthansa, Richard Branson's Virgin Express and Swissair, which last month bought a 44 per cent stake in another regional French airline, Air Littoral.
Liberalisation of the air market now means that any European Union carrier can operate services within another member state.
AOM is based at Paris Orly airport and operates 21 routes. These are largely tourist destinations in the Bahamas, Cuba, Sri Lanka, Australia and the Dominican Republic, although it also operates domestic services to Nice, Marseille, Perpignan and Toulon.
Last year it carried 3.3m passengers and made profits of F27m on sales of F3.9bn.
If the bid is successful it would increase BA's presence in the French market by more than 50 per cent.
Air Liberte operates 42 routes, of which all but four are domestic, and has a fleet of 49 aircraft.
Marc Rochet, chief executive of Air Liberte, said: "This is a carrier we can't afford to ignore, if only because AOM is one of the big operators in the French market."
The sale is one of a string of sell-offs planned by the government.
France aims to raise as much as $2bn this month by selling a stake in Caisse Nationale de Prevoyance, the country's largest life insurer, and plans to follow up with the sale of Credit Lyonnais SA, the country's fifth- largest bank.
Next year it wants to sell part of Air France and shares in the country's largest aerospace company, Aerospatiale.