Ellington, 25, sustained a hip pointer injury last weekend against the Atlanta Falcons, and is still dealing with a foot injury that has bothered him since earlier this season. The second year back did not practice at all this week.
"We're just going to play it by ear," Arians said. "Each guy's got a little package for this one. There's always a surprise here and there."
In 12 games this season, Ellington has carried 201 times, gaining 660 yards and three touchdowns.
"[Fitzgerald]'s practiced all week," Arians said. "He's gotten better each day, but he's still not 100 percent."
Despite losing two straight games, including a 19-3 loss to the division rival Seahawks, the Cardinals remain in first place in the NFC West with a 9-3 record. They host the Chiefs at 4:05 pm EST on Dec. 7.