Bobby Valentine said Crawford is working to get back to form and that appearances in extended spring training games are "imminent" for the left fielder, according to reports.
"I heard he's progressing really nicely," Valentine said. "The way it seems right now, he's feeling very good."
Crawford has been taking batting practice at Fort Myers and will likely begin his extended spring training stint as the designated hitter.
After signing a seven-year, $142 million deal in the 2011 offseason, Crawford had a year to forget, batting just .255 with 11 home runs and 56 RBIs.
The left fielder is hoping to have a bounceback season in 2012, but wrist surgery in January has kept him from playing so far. Barring any setbacks, the Red Sox are hoping to have Crawford back in the lineup by the beginning of May.