Smith recently resumed throwing bullpen sessions, but he's still experiencing back tightness and is without a clear timeline for a return from the 15-day injured list, MLB.com reports.
The Royals placed Smith on the 15-day injured list Monday with low-back spasms.
Smith (0-4) allowed two runs on a hit and a walk over one-third of an inning, taking the loss Friday versus the Cardinals.
Smith was removed from a save situation Friday against the White Sox. He allowed one hit and one walk while striking out one batter in one-third of an inning.
Smith (0-2) was charged with his first blown save of the season Wednesday and took the loss against Baltimore, giving up two runs on two hits and two walks over two-thirds of an inning. he struck out one.
Smith (0-1) was charged with the loss after he surrendered four runs on two hits and two walks during the ninth inning Saturday versus the Twins.
Smith struck out two batters over a perfect inning in his lone Cactus League appearance.
Smith, who signed a one-year, $5 million contract with the Royals in December, is viewed as the leading candidate to serve as the team's closer to begin the season, Ken Rosenthal of The Athletic reports.
Smith agreed to a one-year, $5 million contract with the Royals on Sunday, Jeff Passan of ESPN.com reports.
Smith allowed one walk and struck out one over a scoreless eighth inning in Tuesday's 9-3 loss to the Angels.