Jennings says Stanton saw a hand specialist and was told he could begin so-called "dry swings," with no ball involved.
Speaking before the Marlins played Arizona on Monday night, Jennings called it "step one" in Stanton's rehabilitation. Stanton has been out since June 27 with a left wrist hamate fracture.
Despite the three-week absence, Stanton still leads the National League in home runs with 27 and is third in RBIs with 67.
Asked about a possible return for Stanton in two weeks, Jennings said he didn't "know that there is truly a time frame" but that Stanton will know when he's ready to come back and resume his "tremendous season."