A source confirmed on Tuesday that the Marlins have inquired about the 33-year-old.
Jones was designated for assignment on Monday. If the Marlins move in quickly on the outfielder, a deal could be worked out in the next day or two.
The Padres, according to a second source, also have inquired about Jones.
The Marlins have told the South Florida media that they have no comment regarding Jones.
Jones broke in with the Twins in 1999, and he was in Minnesota through 2005. The left-handed-hitting outfielder was with the Cubs in 2006-07, and the Marlins a couple of years ago explored a deal with Chicago.
Jones got off to a slow start with the Tigers, appearing in 24 games while batting .165 (13-for-79) with one home run, one triple, two doubles and five RBIs.
The Marlins have an outfield concern, as Josh Willingham is on the disabled list with a strained lower back. Willingham went on the disabled list with on May 2, retroactive to April 28. The earliest he is eligible to be activated is May 13 when the club is in Cincinnati.
It still is unclear if Willingham, the team's cleanup hitter, will be ready by then.
If the Marlins add Jones, the veteran would factor into a few roles. He can play all three outfield spots, and he is a candidate to lead off.
A few days ago, the Marlins dropped Hanley Ramirez from leadoff to third in the lineup. For now, Alfredo Amezaga and Cody Ross are platooning in center field. Both are leadoff options.
Joe Frisaro is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.