"He's not far away, but I don't know that Wednesday's the magical day," said manager Bobby Valentine. "It will be sometime soon. He's running in the pool and we'll take it from there."
Ortiz did not speak to the media on Monday.
The slugger had to cancel his planned on-field exercises before Sunday night's game vs. the Yankees after feeling discomfort in the area affected by the injury. As a result, Ortiz worked out in a pool prior to Monday's series opener against the Tigers.
"He was a little sore the day before," Valentine said, "and that's why he went to the pool today to do that running routine."
Ortiz has not played since July 16, when he was hurt rounding the bases on an Adrian Gonzalez home run. The designated hitter has been doing some hitting drills since Friday.
"He's swinging OK," Valentine said. "He doesn't seem like he's lost a lot of his rhythm or strength or timing, but he's only at about 80 percent when he's swinging because he's trying to keep away from making the situation any worse."
Ortiz has been the most productive bat for the Red Sox this year, hitting .316 with 23 homers and 58 RBIs. He was in the midst of an 11-game hitting streak at the time of his injury.