The 21-year-old has been included in the senior squad for the upcoming qualifiers against Montenegro and Poland.
Wilshere, who has won 10 caps for the Three Lions, is yet to play at a major international tournament.
"They are big games and they don't come bigger," he told the Football Association's official website.
"We have a great opportunity to get to a World Cup, and for a young player like me it would be a dream come true.
"There is no better feeling than running out at Wembley in an England shirt, it's what dreams are made of."
England take on Montenegro at Wembley Stadium on Friday night.