Arsenal, who tightened their grip on third place by holding Manchester City to a 2-2 draw on Sunday, need just one point to seal automatic qualification for next season's Champions League.
The fourth-place finishers must win a two-legged qualifier to reach Europe's elite club competition.
"I don't know what happened to Aston Villa this season but I don't expect them to come and just let us beat them," Wilshere told the London Evening Standard.
"We said a few weeks back that we don't want to get fourth. We don't want to have to face a qualifier. We want to be straight in there and enjoy the season without having to play a big game beforehand."
The Gunners have an outside chance of finishing second if they beat Villa and north London rivals Tottenham Hotspur lose at Newcastle United in their final game of the season.
