Webb, recovering from shoulder surgery last year, said he felt "stagnant" after a bullpen session earlier this month. Since then, he's been on a regular three-day plan of long-toss, short-toss and a day off.
The late April target is "definitely not set in stone or anything. It's, I guess, a goal maybe," he told reporters.
Last week, Arizona manager A.J. Hinch said it was growing likely that Webb, the 2006 NL Cy Young Award winner, would not be ready in time for Opening Day.
After his bullpen session earlier this month, a discouraged Webb called Keith Meister, the surgeon who operated on his shoulder last summer. Webb said Meister did not see a problem with his shoulder, but suggested that he ramp back his comeback timetable and spend a week or more playing long-toss before returning to the mound.
"He pretty much said that, 'You just weren't ready to get after it and get on the mound,' " Webb told reporters. "He was like, 'I never had you pegged as an April [return] guy.' He might have told me that before, so he retold me, I guess."
Following his doctor's orders seems to have worked: Webb was pleased with the results from a throwing session on Sunday.
"I was letting it go almost all the way [Sunday]," he said. "I felt like I had more left in the tank. It was good. Really good."
"It's finally good to go back out there and throw instead of just kind of dreading it," Webb added. "It's been good, real good."
Webb pitched more than 200 innings in each season from 2004 through 2008 and never had a significant injury before encountering the shoulder problem last year. He led the NL in victories when he went 22-7 in 2008.
Information from The Associated Press was used in this report.