Cullen is a 19-year-old highly-rated midfielder who has been on the books of West Ham since 2010.
Cullen, who featured in the Europa League qualifiers and against Liverpool at Anfield, wants to get more playing time for the first team.
“With the way the club wants to go it’ll be tough,” the youngster told West Ham’s official website. “We want to be a top six club and the quality of the players here is about as good as it’s ever been, certainly that I can remember.
“It’s a challenge, but one I look forward too, you can always learn from the players that are here as well, that’s a good positive.
"You can always take tips from them and that helps to prove to people that I am good enough to play in the first team.”
It will not be easy for Cullen to get playing time for the West Ham first team as the season progress.
Cullen is only 19 years of age, and perhaps the club chiefs will feel that he is best suited to Under-21 football.
However, West Ham manager Slaven Bilic has already shown this season that he is willing to give talented young players the chance to show what they can do in the first team.
Perhaps Cullen will get his chance in the second half of the season.