Jackson is expected to serve as the designated hitter on Monday before stepping up his outfield work on Tuesday. He'll take an off-day with the Hens on Wednesday before they begin a four-game series at Syracuse the next night.
If things go as hoped, Jackson won't be there for the end of the series.
"There's a possibility he could join us in Minnesota," manager Jim Leyland said, referring to the Tigers' series against the Twins next weekend.
Jackson has been shelved since May 12 with a pulled left hamstring. What was initially hoped to be a short stay on the 15-day disabled list became a four-week absence when lingering soreness prevented Jackson from accelerating pain-free to full speed.