Tillman threw a side session on Thursday in Baltimore -- his second since being diagnosed with right elbow inflammation -- and said it went well, but the organization is being cautious with the 24-year-old righty.
"I think he's going to have one more [side] just to make sure it doesn't flare up," manager Buck Showalter said of Tillman. "That gives us a good feeling about where he is and I think Monday will be a good spot for him."
Sunday's starter is still undecided, as is a pitcher for Tuesday, with Joe Saunders -- Friday's starter -- slated to pitch Wednesday's game. Sunday's start could be one of several different guys, according to Showalter, with Jake Arrieta, Randy Wolf, Steve Johnson and Tommy Hunter all possible options.
Wolf is believed to be the leading candidate to make that start if he's not needed out of the bullpen in the next two games.