The Argentinean, who joined the club from Sampdoria in 2015, has spent most of his time at United as a backup to De Gea.
The 26-year old has been linked with a move to Real Madrid for the past two years, but Romero insists he has no intention of leaving regardless of De Gea's movements.
He said: "I don't know about that [De Gea's future]. But I never want to leave this club because it is so big and I am very happy to stay. I have two years left on my contract and I want to stay here for 10 more years. I want to finish my career here.
"When I came here I wanted to be No 1 but I know what my reality is now. I still work hard every day for my possibilities. When I play, I try to prove how capable I am and that I can do this job. I want to go to the World Cup next year as Argentina's No 1."