The plan could increase the number of seats on its Boeing 777 aircraft by almost 20%, from 280 to 332.
Each row would have 10 seats rather than the current nine.
BA said: "We are flying more customers than ever before... To meet this demand, we are updating our (Boeing) 777 cabins to bring us into line with many of our competitors."
It said it would also be upgrading its in-flight entertainment systems with bigger screens.
There are also reports that BA intends to add a dozen extra seats on its short-haul Airbus A320 aircraft, based at Heathrow.
The latest figures from BA's parent, IAG, showed operating profits in the July to September quarter fell 4% to €1.2bn.
It said the weak pound had cost it €162m (£145m) in the third quarter of the year.
The airline said it expects operating profits for the full year to be up by about 7%, a lower rate than the one it forecast in July.
Its lower profits guidance followed similar moves from rivals Easyjet and Ryanair.