Murray has missed the past five games with a sprained foot. Felix Jones has replaced Murray in the lineup.
Smith suffered a high ankle sprain in Sunday's overtime victory against Cleveland and was replaced by Jermey Parnell. He reported to Valley Ranch on Sunday night for treatment and had more on Monday, but he was not able to practice.
"Depending on how this week goes, basically a game-day decision," Smith said. "I'm trying my best to get back healthy."
Earlier Monday, Cowboys executive vice president Stephen Jones said he doesn't believe Smith or Murray would play Thursday.
"I'm dying to know right now," Jones said of their availability on KRLD-FM. "But I'm really thinking it's probably a long shot for either one of those guys to play."
Later in the interview, Stephen Jones added, "My expectations would be that it's a long shot for either one of them."
ESPNDallas.com's Todd Archer contributed to this report.