The Spaniard had a difficult start to his career at Old Trafford following his arrival from Atletico Madrid in 2011.
However, the 23-year-old has now cemented his place as United's number one shot-stopper, and Woods is confident that De Gea can reach the heights of ex-goalkeepers Peter Schmeichel and Edwin van der Sar.
In an interview with the Manchester Evening News, Woods said: "He has the calmness necessary to cope and the reading of the game and he is gaining so much experience.
"He can become one of the best. He really has done fantastic. He has all the elements to be one of the best."