Hungarian goalkeeper Fulop has impressed in recent months after stepping in for Gordon, who was sidelined with an ankle injury.
Gordon returned to the Black Cats team in Wednesday's FA Cup replay at Blackburn Rovers and kept his side in the game for long periods.
Sunderland boss Ricky Sbragia admits he faces a headache over who to pick in goal against Stoke City on Saturday, but Fulop is hoping to retain his place.
Satisfied"I got the possibility after Craig Gordon was injured," Fulop told MTI. "I was between the posts for six games and then he was back and injured again immediately, and since then I've been the first-choice goalkeeper.
"The competition for the No.1 spot has just started because Gordon is now fully fit, but I'm optimistic because our manager is satisfied with me.
"But Gordon is the most expensive player at the club and that may be a decisive factor, too."
Fulop admits he is now happy at the Stadium of Light and has praised Sbragia since the Scot replaced Roy Keane as manager in December.
He added: "After the change of manager in December, the players found their legs because Sbragia is a more balanced and moderate trainer than Roy Keane and gives more freedom to the players. It's good if you see the results.
"I have a year-and-a-half left on my contract, but now I'm very happy because I can show my abilities on the pitch. If it doesn't change then I'd be happy to stay at Sunderland."