Almirola fractured the T5 vertebra in the middle of his back in a crash in last Saturday's race at Kansas Speedway.
RPM is expected to release Almirola's estimated recovery time at a press conference on Friday.
Almirola appeared at a charity event hosted by fellow racer Martin Truex Jr. earlier this week and touched on his injury, which came in a fiery three-car crash that also involved Joey Logano and Danica Patrick.
"The doctors told me just be careful and don't let anybody give me a hug and all that kind of thing," Almirola said. "For the most part, I'm OK. I've got a broken back and one of my vertebrae is crushed in half, but besides that, I'll live."
Almirola currently stands 23rd in the NASCAR Cup standings, 62 points behind the current 16-driver cutoff for the playoffs.
Smith is currently driving in the NASCAR truck series. Saturday's event will be in his first on the NASCAR Cup circuit this season.
Smith has one career NASCAR Cup win, that coming at Darlington in 2011.