Manager Ned Yost reiterated on Sunday, "We don't know what he's going to do for us yet."
But Finnegan, who threw just one inning on Saturday, will throw again on Tuesday with the intent of him going three innings.
"That's up to him," Yost said. "If he keeps his pitch count down, yes, three innings."
Finnegan is slated to throw about 40-45 pitches.
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @jflanagankc. This story was not subject to the approval of Major League Baseball or its clubs.