"All we will have is a bag drop where passengers can drop off their luggage, otherwise everything will be done online," he told the newspaper.
"Ultimately, we want just one in five people to check-in luggage."
A spokesman for Ryanair told the newspaper that 97 per cent of its customers already booked their flights online and 75 per cent checked in on the web, so O'Leary's announcement was "the logical next step".
Earlier this month, Ryanair said it would cut 200 jobs based in Dublin, including pilot positions as it forecast a sharp drop in air traffic to and from the Irish capital this year.
Ryanair made a loss of almost €119 million ($151 million; Dh556 million) during its third quarter as fuel costs soared and it reduced fares.
However last week the airline also upgraded its full-year profit forecast to between €50 and 80 million from a previous estimate of break-even as fuel costs have fallen sharply since the end of 2008 on reduced demand for energy.