The Bulls are riding a seven-game losing streak.
Rose, who missed Friday's game against the Miami Heat after suffering a sprained left wrist Thursday in Orlando, was severely limited in practice on Monday.
"It's still sore a little bit, but if you want me to go out there and play, I will," Rose said. "That's not an issue for me to go out there and play, but I'm just going to do the smart thing.
"If they want me to wait, I'll wait."
It sounds as if rest will be recommended.
"Right now they're just taking it day by day with me," Rose said. "I've been getting a lot of treatment. [General manager Gar Forman] was telling me don't rush it.
"If anything, wait til this weekend, or this Friday's game. I want to play definitely because it's Memphis [where he went to college]. But if they tell me to wait, I'll wait."
Coach Vinny Del Negro said "probably not," when asked if Rose will play Tuesday.
"I don't know yet," Del Negro said. "We're going to see how he feels [Tuesday] at shootaround, but he didn't do much today, so let's just see how he feels.
"I don't have any perfect answers to this stuff. I don't know when they're going to heal, when they're going to be ready. We want to be smart about it. Hopefully, he'll be able to do something a little bit more in shootaround. Maybe get him a few minutes out there, but if he's only going to be able to play a few, I don't see the purpose."
"The only way we have a realistic chance [at the playoffs] is to get everybody healthy," Del Negro said. "And when that is I don't know. We still got to play well. We still got to find ways to win.
"It's very difficult. I know you guys understand that. It's not fun right now. It's not a lot of fun."
Nick Friedell covers the Bulls for ESPNChicago.com.