Cobb was struck in the right ear by a liner hit by Kansas City's Eric Hosmer on June 15. He underwent the test Wednesday.
He said he hasn't gotten the results of the test back, but is optimistic he could be cleared to throw to hitters soon.
"MLB and the union have to get together and decide on that, but my doctor said I did really well on it," Cobb said Thursday before the Rays played Minnesota. "I've had two or three of them and I assume that's the last one."
Cobb had his third bullpen session since being hurt on Thursday.
"It's still up in the air whether it'll be just another bullpen or maybe a live BP, I'm not sure yet," Cobb said.
Cobb said it's possible he could rejoin the Rays' rotation next month.
"I definitely think early August is realistic," Cobb said. "Late July might be a little bit of a push but you might as well set your goals high and hopefully it'll happen."
Cobb's first test against hitters will come from behind a protective screen, a regular practice for injured pitchers. He had balls hit at while behind a screen Wednesday.
"It was pretty scary," Cobb said. "The first one seemed like it came back a lot faster than it did, but after three or four it became normal again and felt pretty good."
Cobb said his vertigo symptoms have not affected his mound work.
"Still have vertigo a little bit, but I don't think pitching aggravates it," Cobb said. "There's a few things we're trying to speed it up, but over time it'll go away."