Lletget, 20, signed his first pro deal with the Hammers in September 2010, and he has become a fixture on the club's Under-21 developmental squad. He has also been selected for the first team by manager Sam Allardyce on five occasions -- including once against Manchester United -- but he has not featured for the senior squad on the field.
"I sure feel my debut's coming," Lletget told West Ham TV. "All I can do is get my head down and keep doing what I'm doing. I know it will come. As long as the first-team keeps getting results, we'll get in a comfortable position, which is what the whole club wants. Then I'm sure I'll get my chance.
"It has been what, five years or something like that at West Ham, and I just wish I can stay here for as long as I can.
"I was quite relieved [to sign the new deal]. Obviously my contract was running up this year. So in the first half of this season, I was just trying to impress the manager really, and fortunately everything worked out."
Lletget was a member of the U.S. U-23 player pool during the last Olympic qualifying run, and he told West Ham's official website that he would be open to a loan move if the circumstances were right and as he gains more notoriety.
"Sooner or later, a club will show some interest, and it will be the right move, a good loan wouldn't be a bad idea," Lletget said. "My mind is a bit settled. I feel good at the moment, everything's working out."