Although BA's chief executive, Bob Ayling, refused to comment last week, the talks are at an advanced stage, according to senior management sources at the airline.
Air One is 98 per cent owned by the Italian construction magnate Carlo Toto. The low-cost carrier began domestic operations in November 1995 and has since picked up a near 30 per cent share of the Rome-Milan route. It is due to launch a new service from Rome Milate airport to Stansted in co-operation with Air UK at the end of this month. It has a fleet of six Boeing 737s and two McDonnell Douglas aircraft.
If the deal comes off it will have serious implications for Alitalia, which is awaiting European Commission approval for a 3,000bn lira injection of state aid to help it restructure.
BA already has a foothold in Germany and France through its subsidiary airlines Deutsche BA, TAT and Air Liberte. Two years ago it held talks about entering the Italian market through a franchising deal with Meridiana, which is owned by the Aga Khan and based in Sardinia.
"If you compare the Italian and French markets, TAT is like Meridiana and Air Liberte is like Air One," said one source. "BA has encountered some difficulties with its acquisitions in France and Germany and it is for this reason that Air One is a perfect acquisition because it is a low-cost carrier."
A decision on Alitalia's state-aid application is not expected until the end of July. BA has protested strongly against the airline being given further support along with Lufthansa, British Midland and Virgin Express.
Losses from Deutsche BA rose last year due to restructuring costs, a declining air traffic market and the weakening of the German mark against sterling. Despite this, Deutsche BA gained market share on domestic routes, launching services from Munich to Hamburg and Cologne and also began flights from Germany to Gatwick. TAT, meanwhile, more than halved its operating losses as passenger numbers increased by a third on domestic routes and by a fifth on services to Heathrow and Gatwick.