The Premier League leaders top the table by two points, with Wilshere starting seven of their 11 top-flight matches this term, scoring twice.
Wilshere believes the number of leaders available to manager Arsene Wenger lends their title bid huge strength.
"From the team that I first broke into a lot of them have gone so I'm one of the few who's been around, there's Bacary (Sagna) as well but I'm one of the only midfielders who has been around for a while," he told the club's official website.
"Mikel (Arteta) came in, he was the captain at Everton and he's the vice-captain here and you can tell by the way he is off the pitch, even when he was injured he was in the dressing room and giving us support.
"I do feel a bit of responsibility but I have players around to help me."
Wilshere hopes to be handed the captain's armband at the Emirates Stadium in the future, as he seeks to help Arsenal win their first trophy since lifting the FA Cup in 2005.
"I've grown up at this club and I have captained the club at under-16 level, under-18 level and last season as well I got the armband for 20 minutes or so (against West Ham in January) which was a nice feeling," he added.
"I want to do that (be a leader) for this club."
