Dockett made the comments in a series of messages posted on his Twitter page Monday.
He said he met recently with team officials and came away confident. Dockett has three years remaining on his contract, but wants a new deal.
He didn't participate in the team's voluntary workout this summer. Dockett, along with wide receiver Anquan Boldin, sat out minicamp with what the two said were groin injuries.
The Cardinals have said linebacker Karlos Dansby is their next target for a new contract, then the team will turn its attention to Boldin, who has two years left.
"From the first day of training camp and on, I will not let my contract issues distract me or my team from reaching our goals," Dockett wrote. "I also look forward to playing with my teammates and defending our NFC championship title, and I am looking forward to a great season."
Dockett said the idea to post his feelings via Twitter was his, and did not come from his agent Drew Rosenhaus.
"WE WILL WIN THE NFC WEST," Dockett wrote.