Arsenal have ended the year on top of the Premier League table on three previous occasions in the last 14 years but they could not go on to win the title in any of those seasons.
"It shows you that we have a good chance as the statistics show you that eight of the past 11 years the team who was top on New Year's Day won it," Wenger told reporters.
"I believe that we are mature enough and that we have the requested quality to fight and compete.
"You question our mentality, I don't. We have to rise above that and show that we can deal with all that and I believe we have to be guided by playing better football and being a real team in every game and show that we can be competitive.
"The most important thing is to feel, at the end of the season, that we have given absolutely everything to be successful.
"After that, if somebody has been better than us, we will accept it, but we want to fight to show that we have a chance.
"I will remind you that only one team won the league without losing a game. That is Arsenal Football Club. It is not the date (New Year's Day) that is decided you win the league.
Arsenal last won the league in 2004 when the famous "Invincibles" side romped to the title without losing a single game that campaign.
Wenger's men host third-from-bottom Newcastle United in the league on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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