The young Spaniard has struggled to cope with the physicality of the Premier League but his performance against Madrid at the Bernabeu was impressive.
Casillas, who is regarded as one of the best keeper in the world, has been injured with a broken hand and Madrid are planning to bring in De Gea as his long-term successor.
De Gea, 22, is an excellent shot stopper but lacks the ability to deal with set-pieces. United boss Sir Alex Ferguson was furious with the youngster after his mistake led Tottenham equalise but his performance against Madrid in the Champions League tie kept United in the game.
United paid £17million for De Gea two years ago but are already plotting a move for Stoke keeper Asmir Begovic in the summer with the Potters signing Birmingham's Jack Butland who has returned to the club on loan.
Begovic is open to a move to Old Trafford but Arsenal are also planning to move in for the Bosnian. Apart from the Stoke stopper, United are eyeing Sunderland's Simon Mignolet and Swansea's Michel Vorm.
With Madrid planning to replace Casillas, their fierce rivals Barcelona also need a keeper to come in for the departing Victor Valdes. The Catalans are favourites to sign Liverpool keeper Pepe Reina but could move in for De Gea if United decide to sell.