Bogans has an option for $1.73 million, but the Bulls have been searching for an upgrade at the shooting guard position since teams could start making contact with agents last week.
Bogans started 82 games for the Bulls a season ago, averaging four points and two rebounds a game.
The Bulls figure to hold out as long as they can regarding the decision on Bogans' contract, given that they are waiting to see how the rest of the market for two-guards shakes out.
"I think we just have to be patient, see how it plays out," Bulls coach Tom Thibodeau said on Friday. "It's an unusual set of circumstances right now, and we just have to be patient.
"I've said it all along, he did a great job for us. He did his job every night, played great defense. Hit spot up shots. He's the consummate professional."
The Bulls invited back Brian Scalabrine, who spent all season with the Bulls last year and was well-liked in the locker room because of his personality and his ability to help players understand Thibodeau's system.
After the NBA season ended, Scalabrine went to Italy to play before leaving the country recently to try and latch on in the NBA for another season.
Nick Friedell covers the Bulls for ESPNChicago.com and ESPN 1000.