Cobb, struck in the right ear by a liner hit by Kansas City's Eric Hosmer on June 15, threw off a mound for the second time since being hurt before Monday night's game against Minnesota.
"The timeline is, obviously, getting shorter for me and that's exciting," Cobb said. "Hopefully early August, maybe end of this month would be a pretty nice expectation. Right now, I am trying to get there as soon as possible."
Cobb is scheduled to have another bullpen session Thursday and hopes to face hitters soon after that.
"I'm pushing them to let me do it," Cobb said. "I'm trying to speed up this process as much as I can now that I feel good."
Cobb had his initial mound session last Friday. His first time against hitters will have him throwing from behind a protective screen, a regular practice for injured pitchers.
"It will be one of those situations where I'm gradually put into it and I'll be able to handle the situation when it comes," Cobb said. "I'm extremely anxious to get out there and face hitters. No concern in my mind right now that I'll be worried when I do face them, so I'd like to get out there as soon as possible."
Cobb said his vertigo symptoms have greatly improved.
"That's gotten immeasurably better in the last two days," he said.