"I'm hopeful," Gibson said. "I'm always hopeful. This is where I want to stay, this is where I hopefully want to retire one day. So we'll have to wait and see."
Gibson's agent, Mark Bartelstein, told ESPNChicago.com on Thursday that talks are ongoing.
If a deal is not worked out by the deadline, Gibson would become a restricted free agent at the end of the season and be able to sign an offer sheet that the Bulls would have the option to match.
Gibson, who likely would command between $8-$10 million a year in any new deal, says the negotiations have not been on his mind.
"I haven't even really thought about it to tell you the truth," he said. "The last couple days I haven't even heard any ... that's the last thing on my mind. My focus is on just winning games, and (I'm) ready for the season to start."
With Omer Asik gone, Gibson is being asked to be more of a low-post threat by Bulls coach Tom Thibodeau. After nearly everyone was off the floor following Thursday's practice, Gibson spent additional time working on his post moves.
"Just working on fundamentals, back-to-the-basket stuff with contact, just daily routine, just trying to get my timing right," Gibson said. "Thibs really wants me to get down in the paint. He wants to get the ball down to me. We do this before practice, after practice. Just having a steady routine. I know it's preseason, but you can never get days off. It's about getting better every day."
Despite his extra work, Gibson is averaging 7.5 points and shooting 32.1 percent from the field through four preseason games.
So far, Gibson isn't worried. His preseason numbers have varied in his previous three years.
"I'm just trying to take my time, letting the game come to me," Gibson said. "Trying to take some open looks every now and then. It isn't going good so far from the shot standpoint. But I look at how I've been playing this preseason the last couple years. Just trying to let my game come to me and just take it in stride, learn from it and come back to practice the next day and go even harder."
ESPNChicago.com's Scott Powers contributed to this story.