But the Republic of Ireland under-21 international has not ruled out the possibility of going somewhere on loan to get first team experience as well.
"To be fair, I'm not too sure what is happening yet," he says, "and the reserve match at Chelsea on Monday was my first proper game for a month, so I've just got to wait and see.
"There were people there watching so if I'm going to go it will be soon."
Indeed Shaun, just back from another injury - he could be classed as one of the unluckiest players at the club on that score - is hoping, whatever happens, to have a change in fortunes as he looks to build a career in professional football.
"Every time I say I am fit now I end up getting injured again, so I am not going to say anything about it. It has happened about four times now, but that's what happens in football," he shrugs.
"Hopefully I will stay fit and if I don't go on loan I will keep doing well in the reserves and I get another chance to prove myself.
"Glenn has definitely offered me a couple of years and I want to stay, but you are at the age now where you have to start playing first team football, and when that happens you might have to go somewhere else to do so.
"But I want to stay and hope everything goes all right. Nothing has been sorted out yet, but I like it at West Ham and I'm still enjoying it here."
The contract offer is a timely boost for Shaun, who has been at the club for nearly five years and made his debut as a substitute against Newcastle in January 2000.
The 21-year-old adds: "At least you know you are still in his thoughts, otherwise you wouldn't be offered it in the first place and it is nice to know that. It gives you another couple of years' security and the chance to impress and see what happens."
Shaun played his part in an unlucky defeat against an experienced Chelsea reserve side on Monday, and he says: "Glenn has kept all the youngsters together and we have near enough got the same team every week, so people are getting to know each other a lot more, whereas last year there were trialists coming in, and you didn't know their names half the time.
"But at least this year the team has been kept together, and it has been proven right because we were coming bottom near enough every year. This time we have beaten some good teams, and the boys are enjoying it a lot more as well.
"You always learn and develop every day, especially when you are playing with the quality players we have got at the club."