The actor revealed that he may not appear in the next 20th Century Fox movie in the franchise.
"I don't know whether or not I will do this next movie," he told Vanity Fair.
"I am really proud of [The Wolverine] and I am excited to develop something with Jim Mangold from the beginning because that is a great ride.
"That's exciting, to see what we come up with but I have a very high expectation of what it would need to be [for me to star in it] and if it doesn't reach those, I won't be doing it."
He also revealed that he shot his dialogue for The Wolverine in the morning when he was "naturally grumpier".
Fox announced a third Wolverine film following the debut of the James Mangold movie earlier in the year.
Jackman previously revealed that he is no longer contracted to appear in the role.
He will next be seen as Wolverine in X-Men: Days of Future Past, which will arrive in UK cinemas on May 22, 2014 and the US on May 23, 2014. Watch a trailer for the film below:
Catch up on all the latest TV and Movies releases in Digital Spy's Screen Time: