"We have to fight like mad to win our games," the Frenchman told a news conference before they host 15th-placed Leicester City in the league on Wednesday.
Wenger has led his side to a top-four finish every season since joining the club in 1996.
"The door is open but it demands a consistency from us," Wenger said.
"It is still possible, but we need a near perfect run-in. We need to keep the level of desire and hunger for every game of the season."
The British media reported on Monday that French club Olympique de Marseille are looking to sign Arsenal striker Olivier Giroud at the end of the season.
Wenger, however, said he had heard no such thing and the 30-year-old France international signed a contract in January which keeps him at the Emirates until 2020.
"I have had no approach from Marseille, and we want to keep Olivier Giroud at the club."
The 67-year-old Wenger, whose own contract expires at the end of the season, gave no updates on his future but said he was evaluating transfer targets for Arsenal's next campaign.
"Yes, of course. I work until the last day of the season for the present and the future.
"What happens with me is a bit secondary, what is important is the future of the club."
Following the Leicester encounter, Arsenal travel on Sunday to their north London rivals, second-placed Tottenham Hotspur.
(Reporting by Hardik Vyas in Bengaluru; Editing by Hugh Lawson)
Share
