Jackson, 32, met with the Patriots on Wednesday and worked out with the team the following day, sources told ESPN last week. He has not played in the NFL since being released by the Atlanta Falcons in February.
Jackson tweeted Monday for the first time since September, posting a photo of himself working out accompanied by the caption, "I'm back." He later updated his Twitter page and called himself a "New England Patriots running back."
No announcement was made by the team, which isn't required to do so until the contract is official.
The 6-foot-3, 230-pound Jackson could provide depth to the Patriots, who already have placed running backs LeGarrette Blount and Dion Lewis on season-ending injured reserve this year.
The first-place Patriots (12-2) used a committee at running back in Sunday's victory over the Tennessee Titans, dividing reps among Brandon Bolden, James White and rookie Joey Iosefa, who was promoted from the practice squad Saturday.
A three-time Pro Bowler, Jackson has rushed for 11,388 yards in parts of 11 seasons with the Falcons and the St. Louis Rams. He previously played for current Patriots offensive coordinator Josh McDaniels when the two were both with the Rams.
Information from The Associated Press was used in this report.
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