The right-hander was placed on the DL on June 4 with a right shoulder strain. He threw from 120 feet on Friday and plans to throw again on Sunday as he continues to work through a rehab program.
"I'm hoping by the end of next week there is a kind of progression and I'll [throw] off the mound," Pavano said. "I don't want to get too far in front of myself."
Pavano struggled in 11 starts before being shelved, going 2-5 with a 6.00 ERA.
"It's no fun being in this position," he said. "It's an opportune time to be a starting pitcher for the Minnesota Twins. They need me. That's why they signed me for two years. It's been frustrating for me not to be able to go out there and compete for my team."
The 36-year-old served as the Twins' Opening Day starter. He is also one of 11 starting pitchers Minnesota has used this season.
"I'm letting myself down," he said. "I'm letting everyone down around me. But there are things that are out of my control right now. I had an injury that I gave every opportunity to get better and it wasn't getting better by pitching. I got to the point that I had to get it better. It just takes times, as frustrating as it can be. Sometimes it takes more time than expected."
Twins manager Ron Gardenhire also emphasized the importance of patience.
"The big thing is trying to stay away from setbacks," Gardenhire said. "Start doing too much and then we have a setback or something, you don't want to go there. We want to make sure he's healthy before he gets out there and starts really letting it fly."