The 25-year-old, who took a break from rugby in June after suffering a series of concussions, scored 17 and 27 points and played for 80 minutes in both matches for his club.
"I definitely feel I could be part of the training squad. I feel good enough. These games have been very beneficial," Barnes, who has won 31 Test caps, told Monday's Australian newspaper.
Australia coach Robbie Deans, who supported Barnes's decision to take time out from rugby, will name his squad for Saturday's test against the All Blacks in Auckland on Tuesday.
"I haven't spoken to Robbie Deans yet," Barnes added. "I'll speak to the powers that be. The Wallabies have a test against the All Blacks this week. I'm the least of their worries."
Although Quade Cooper remains Australia's first choice at fly-half, a fully fit Barnes would be a strong contender for the World Cup squad as back-up, with his ability to also play fullback and centre adding to his value.
Matt Giteau, another option at fly-half or inside centre, was dropped by Deans after a poor display in the defeat to Samoa which kicked off the Wallabies season.
The 28-year-old, who has played 92 times for his country since his debut in 2002, is still hopeful of having a crack at playing at the World Cup.
"I feel like I am training well and I am certainly confident that if I got the opportunity to play I could step up and perform," he told the Daily Telegraph.
"It's a little bit unfamiliar for me, I have never really been in a situation like this.
"You just have to do the best you can in training, be as positive as you can for the group and whatever happens, happens. I guess we will just have to wait and see."
Deans will name his World Cup squad on August 18.