GLENDALE, Ariz. -- It appears Zack Greinke's first regular-season start for the Los Angeles Dodgers will be pushed back by at least a few days and possibly longer.

The Dodgers said the former Cy Young Award winner felt strong Monday, a day after his first bullpen session since receiving an injection in his pitching elbow.

After signing a $147 million, six-year contract with the Dodgers as a free agent, Greinke has appeared in just two spring-training games for a total of five innings. Greinke pitched on Feb. 24 and March 1, then was slowed due to inflammation in his right elbow and received an injection of platelet-rich plasma and anti-inflammatory medication on March 11.

"He felt good this morning," Dodgers manager Don Mattingly said Monday.

Greinke is scheduled to pitch again on Wednesday, possibly in a simulated game at the minor league complex on a day the Dodgers play Kansas City at Surprise.

"We're not sure just where, but we want to control the outing," Mattingly said.

Greinke threw 38 pitches in Sunday's bullpen session and is expected to throw 45 pitches Wednesday.

He could pitch again on March 25 against the Royals in Surprise and March 30 at the Los Angeles Angels, which would line him up to make his regular-season Dodgers debut April 5 -- if he has enough arm strength. Greinke originally had been slated to start April 2 against San Francisco.

NOTES: RHP Chad Billingsley, who bruised the index finger on his throwing hand during a bunting drill Friday, could miss Tuesday's scheduled start against Oakland. "It's day to day," Billingsley said. "But right now the command is not there." X-rays were negative.