Conte has been ruled out for between four and five months after undergoing shoulder surgery in March, meaning that he will miss the entire off-season programme.
However, Emery has backed Conte to recover from his injury and challenged him to improve in order to earn an extension to his current contract.
"I think the number one thing for Chris making improvements is Chris himself. I'm not counting on other guys getting better to help another player improve," Emery is quoted as saying by ESPN.
"It's on them each individually, and obviously collectively. If we improve individually, we'll improve as a group. Chris knows he has to come in and compete to start.
"My vision for him is that he does compete and win it. I'd love to be talking to him about an extension. So let's see what he does."
Conte was selected in the third round of the 2011 Draft and has since appeared in 45 games for the Bears.