"Next season I want to play every single match because my aim is to be the first-choice goalkeeper of the Hungarian national team," Fulop told Origo.hu.
"I think I can do it in Sunderland or at another club.
"I went around the block this season at a club which was 17th on the table and then won the championship.
"It's true that I didn't get so much possibility [to play) as I wanted but I got to know very good company at the club.
"Roy Keane is a big-name personality in football, he's a pure professional and one can learn a lot from him.
"But this summer I plan to talk to my manager, I turned 24 this May and I think I'm capable of doing big things in goal.
"If I can't do it in Sunderland then I may change club - fortunately I have a few offers.
"When Sunderland signed me I had been told I would be a first-choice keeper for a long period at the club.
"I do my best at training - Keane confirmed this too - and I think in the games I played I had good displays.
"At the end of the season he [Keane] said to me that he wanted me to fight for my place in the team and of course I want to match his needs.
"I have offers from many countries but England has the priority because I know the conditions and possibilities of the country so I would like to stay here [in England]."