The Hammers beat Arsenal 2-0 on the opening day of the season, and they have continued to progress since that victory, moving into third place in the Premier League table.
Wilshere believes that West Ham have a lot of quality in their squad, and he says that if they didn't finish in the top-half, they would be disappointed.
"They've got great quality. I think they'll be disappointed if they didn't get in the top-ten," the England international responded, when asked where West Ham would finish this season.
"We played them first game of the season and they were amazing. They then had a few disappointing results at home, but they seem to have turned that around.
"Growing up I was a West Ham fan and a lot of my family still are, so they're delighted. With players like [Dimitri] Payet, they're players you want to see more of."
As well as beating Arsenal, West Ham have also claimed notable scalps over Liverpool, Manchester City and Chelsea already this term.
They are the second top scorers in the whole of England's top-flight, and Slaven Bilic has the side playing some of their finest football in recent memory.
The Hammers are currently just two points behind top of the table Manchester City, and they have some winnable looking games coming up.
West Ham's next two matches are against sides in the bottom-half of the Premier League table, with Bilic's men set to take on Watford at the weekend, before they host Everton.