The Spaniard replaced Thomas Vermaelen as skipper after the Belgian became the fifth captain in nine years to be sold by Arsenal.
With less than 12 months to run on his current deal at the Emirates Stadium, Arteta has been linked with a move to Athletic Bilbao.
Wenger's policy of offering just one-year extensions to players over the age of 30 has previously seen several stars leave, but the Frenchman is sure his current captain will not join that list.
He said: "You know the policy, nobody accepts it. But even [players] at 75 you ideally want to sign for one more year!
"He is a strong personality, Mikel Arteta. I don't really doubt that he will extend his contract, but at the moment it is not done."
Arteta joined Arsenal from Everton in 2011 and has gone on to play 124 times of the Londoners.
He featured in all but one of their FA Cup games last season as Wenger's trophy drought was ended courtesy of a 3-2 Wembley win over Hull City.
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