"We have the ambition, we have the desire, we should have the confidence from last season - so we have a good basis. It's now up to us to make sure we have the right attitude and the right hunger to go for more," he told the club's official website.
"In the Premier League [last season] we were not far away, we got 79 points and with what happened to us with injuries, I feel that we did quite well.
"On top of that we won the FA Cup so I think it's a good platform to go for more, but in the Premier League everybody tries to improve the team and it's very difficult to predict what will happen this year."
Wenger is expected to add more new recruits to his squad before the season begins, with Nice goalkeeper David Ospina rumoured to be next on his shopping list.