If McCown performs well enough during practice this week, he will get the start, according to the sources.
"I have no idea," McCown said when asked if the staff indicated he'd start against the Packers. "I'm just gonna get myself ready like I've done every week, and then we'll see what happens."
Caleb Hanie threw three interceptions -- with two being returned for touchdowns -- in a 38-14 loss to the Seattle Seahawks on Sunday, which extended the Bears' losing streak to four. That gave Hanie nine interceptions in the four games since Jay Cutler fractured his thumb. The Bears' offense has scored just 40 points over the last four games.
McCown, who was acquired on Nov. 23, replaced Hanie for the last two drives Sunday and completed just one pass and threw an interception. Since 2007, McCown has attempted just eight passes, completing two.
"We're trying to win a football game, so the best guys who give us an opportunity to do that will be on the field," Bears coach Lovie Smith said on Monday. "No more than that."
Smith was non-committal when asked Monday who will start.
Jeff Dickerson covers the Bears for ESPNChicago.com and ESPN 1000. ESPNChicago.com's Michael C. Wright contributed to this report.