Pineda has not pitched in a big league game since April 23, the day he was ejected from a start against the Red Sox at Fenway Park for having a large smudge of pine tar on his neck.
He accepted Major League Baseball's 10-game suspension for the incident, then strained a muscle in his upper back while throwing a simulated game in an attempt to stay sharp.
Yankees manager Joe Girardi said that he believes Pineda would probably throw in one more extended spring game if Tuesday's outing goes well, bumping up to three innings, and then could be cleared for Minor League rehab starts.
"I think when you start to see him throwing three and four innings, and bouncing back, you know that he's getting fairly close," Girardi said.
Pineda had a 1.83 ERA in four April starts before the suspension and the injury. Girardi said that the Yankees are eager to get him back, but they would want Pineda to build up to throw 75 to 85 pitches before he would be added to the active big league roster.
"As long as he has no setbacks, he'll be coming pretty quickly here," Girardi said.
Pineda missed all of the 2012 and '13 seasons following right labrum surgery. Because of that, the Yankees thought they might have to scale back his outings later in the season, but Pineda's stint on the disabled list has erased that concern, assuming that he can come back healthy.
"We never set a limit on innings," Girardi said. "It was more of how he's doing physically and watching his stuff, but he's missed a substantial period of time here. You would think that he'd probably be able to go out most of the year."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.