Coach Ken Whisenhunt would give no timetable for Wilson's return other than to say he expects the four-time Pro Bowler to play this season.
"That's one thing that is encouraging," Whisenhunt said. "It's just going to be a matter of how his body responds to the rehab. So far it's been very good."
Wilson, in a sometimes-playful post-practice session with reporters Monday afternoon, wasn't making any promises but is targeting a return in time for the team's season opener Sept. 11 against Carolina.
"I would love to be out there the first game. I would love to do that," he said. "That would be great. I've got a roster bonus coming up. I've got some things that depend on that, so I'd love to be out there the first game."
The 31-year-old safety, who has played all 10 of his NFL seasons with Arizona, was injured in Saturday's scrimmage while attempting to tackle running back Beanie Wells. He didn't even want to talk about the surgery option.
"No, no surgery," he said. "That's negative. I'm dealing with positives right now. That's a negative statement."
Whisenhunt said he didn't know how long the Cardinals would give the rehab process before deciding whether surgery would be necessary.
"I can't say if it's a week, two weeks, three weeks. I can't tell you what that is," Whisenhunt said, "because I don't know. I know this. My No. 1 concern is the health of Adrian. I know he's a very tough player and he'd go out there with one arm if he could. So we have to obviously make sure that his body is healing correctly before we allow him to play."
Rashad Johnson, a third-round draft pick out of Alabama in his third season with Arizona, moves up to Wilson's place on the depth chart.
"Listen, this business is all about the next guy being able to step in and play," Whisenhunt said. "Rashad's been here working very hard for a couple of years and if he gets this opportunity, I wouldn't be surprised at all if he does a very good job with it."
Wilson immediately began rehab exercises once an MRI showed the extent of the injury, including work on the field while the team practiced.
"As you saw today, he's going to work as much as he possibly can to get back as quickly as he can," Whisenhunt said. "I've learned in this business you can't ever rule somebody out or say for sure somebody's going to play. You've got to see how everybody responds differently."
Although he made the Pro Bowl, Wilson considered last year a subpar season. Although he would not use it as an excuse, he was bothered by an abdominal injury much of the way.
"I can play hurt," Wilson said last week. "Regardless of what happens to me on the field, it's my responsibility to the team to be a leader, to be out there and show those young guys that even though you're hurt, you can still play through things like that. Really, that's my whole message."
A team captain, Wilson is the longest-serving member of the Cardinals. He endured the years of losing before the stunning turnaround that led to the Super Bowl appearance in the 2008 season and an NFC West title the following year.
"I know what type of player that I am," he said last week. "I know I'm a top 50 player in this league. So I'm just going to go out there and do my thing and let my play speak."
In another injury development, backup cornerback Michael Adams underwent arthroscopic knee surgery. No timetable was set for his return, either.