The plans under consideration at Ludgate House call for the Sunday Express' price to be cut from £1 to 50p, undercutting the £1.10 price of the Mail on Sunday.
The Saturday edition of the Express would fall from 50p to 25p, 35p cheaper than the Saturday Mail. It is believed the changes could come into force as early as this weekend.
The move follows the news that Express Newspapers will launch a Sunday Star before the end of the year.