"He's good enough to keep thinking about it," Sveum said Thursday, when asked if Dempster was good to go.
Dempster has been on the disabled list since June 16 with a sore right lat, and he threw his second bullpen session on Wednesday. Sveum will make a decision prior to Friday's game.
The Cubs' other option on Sunday is Chris Volstad, who struggled in 4 1/3 innings in Tuesday's 10-3 loss to the Braves. Sveum wasn't happy with Volstad not following the game plan, and the two talked.
"Everything's fine," Sveum said. "It was a good talk. It was a little bit about everything. It's just a matter of talking to him about letting the catchers do their job, and he agreed. He agreed that sometimes he gets a little out of whack on the mound and this and that, and we'll leave it at that. He agreed he needs to trust them, and not that he doesn't trust them, but he gets on his own path sometimes."
Volstad (0-7, 7.94 ERA) has gone nearly a calendar year without a win. His last came July 10, 2011, against the Astros.