Manager John Farrell told reporters before Tuesday's game with the Miami Marlins that the Red Sox hope Uehara will throw off flat ground and then complete a bullpen session by the weekend.
Farrell acknowledged that time is growing shorter for Uehara to be ready to pitch by the regular-season opener in Philadelphia on April 6.
"With each passing day that he's not in a game, there's growing concern in the sense of, 'Will he be ready for April 6?' We're just working through that," Farrell said.
"Three games next week would give him six appearances in spring training. Is that enough? We just have to evaluate the stuff once he gets back in games."
Uehara, who turns 40 on April 3, has saved 47 games in two seasons with the Red Sox. He finished seventh in American League Cy Young Award balloting in 2013, made the All-Star team last season and has 181 strikeouts and only 17 walks in 138⅔ innings with Boston.
Uehara last pitched on March 14, and he has logged only three innings of work in spring training. If he begins the season on the disabled list, the Red Sox can backdate the assignment to March 27 -- 10 days before the opener. That would allow the team to activate Uehara during Boston's second series of the regular season against the Yankees in New York.
Edward Mujica, who has 49 career saves over nine big-league seasons, is the leading candidate to fill in at closer until Uehara is ready.
Farrell also said Tuesday that David Ortiz continues to work his way back from the flu and should return to the lineup Thursday against Minnesota. The Red Sox are also targeting a return to action later this week by first baseman Mike Napoli, who has missed several days with right ankle soreness.