And the Brewers' 40-man roster is "more than full," Ash said of a roster that's at capacity, plus three players on the 60-day DL.
Manager Ron Roenicke said the team would announce its intent in the next couple of days, though it could go all the way to Tuesday, when the Brewers play the second of four games at Dodger Stadium.
He alluded to a desire to leave Parra in the bullpen, where the left-hander has a 3.70 ERA in 19 appearances this season, with 25 strikeouts versus nine walks.
"I really like what he's doing in the bullpen right now," Roenicke said. "Even if we have someone else start it and we have [Parra] piggyback, I would probably feel better about it, just because I know what he's doing for us so far."
That would seem to put Fiers and Peralta at the front of the line.
"They've had flashes of brilliance," Ash said. "It's just been rare that [they go] innings one through seven or eight, clean. There's always some hiccup."
Fiers provided an example Thursday night against Las Vegas, allowing four first-inning runs on three hits -- including back-to-back homers -- then retiring 19 of the final 20 batters he faced. He is 1-3 with a 4.55 ERA and a team-best 49 strikeouts in 10 starts, and is already in line to start Tuesday.
Peralta, the Brewers' consensus top prospect entering the season, is 1-5 with a 5.62 ERA in nine inconsistent starts for Nashville. He is currently scheduled to pitch Sunday.
Also at Nashville is right-hander Mark Rogers, who is 0-2 with a 5.29 ERA in seven starts. He is also on the 40-man roster.
Down at Huntsville, Thornburg is 6-0 with a 2.28 ERA in 10 starts, with 59 strikeouts and 20 walks in 59 1/3 innings.
"His name has definitely come up," Roenicke said. "I talked to Rick [Kranitz, Milwaukee's pitching coach] today about him a little bit. If [Thornburg] had been with us in Spring Training and been lights out in Spring Training, it makes you feel a little bit better. When he pitched, he was a little nervous, which they should be. Those first times, these guys want to show us something. Nerves play into it a lot."