Manager Don Mattingly said on Thursday that Eovaldi would make "a couple more starts" before moving to the bullpen.
"Well, we're not going to shut him down completely," Mattingly said. "We really want him to finish up. We'll probably pitch him out of the bullpen."
In three starts, Eovaldi is 1-1 with a 2.12 ERA, giving up only 11 hits and nine walks in 17 innings.
"He's a young guy with a bright future," Mattingly said.
Eovaldi also pitched 103 innings for Chattanooga in the Double-A Southern League. Last year, he pitched 98 1/3 innings for three Dodgers Minor League teams.
"You want to increase their innings each year by a percentage," Mattingly said.