The planemaker’s latest short-haul jet has been grounded since March following two fatal crashes.
A total of 346 people died when Boeing 737 Max jets belonging to Lion Air and Ethiopian Airlines crashed shortly after take-off.
In both cases, an anti-stall system known as MCAS forced the nose of the aircraft downwards despite the pilots’ best efforts to fight it.
Boeing is working on software and training updates, but at present there is no certainty about when the plane may fly again.
At the Paris Air Show this week, British Airways’ parent company, IAG, said it wanted to buy 200 of the planes.
Subject to a commercial contract, the mix of 737 Max 8 and 737 Max 10 aircraft would be delivered between 2023 and 2027.
IAG said: “It is anticipated that the aircraft would be used by a number of the Group’s airlines including Vueling, Level plus British Airways at London Gatwick airport.”
At present BA flies no short-haul Boeing aircraft. The fleet at Gatwick and Heathrow is all Airbus A320 series.
Willie Walsh, IAG’s chief executive, said: “We’re very pleased to sign this letter of intent with Boeing and are certain that these aircraft will be a great addition to IAG’s short-haul fleet.
“We have every confidence in Boeing and expect that the aircraft will make a successful return to service in the coming months having received approval from the regulators.”
The biggest operators of the 737 Max in the UK are Tui Airways, Norwegian and Ryanair.