Harrison, 39, played the final regular-season game and all three postseason games with the Patriots after the Steelers released him in late December. He played 69 of 75 defensive snaps in Super Bowl LII.
Following the loss to the Eagles, Harrison said he would “want to come back wherever I’m wanted.”
The Patriots have limited cap space but a big need in the front seven of their defense after ranking 29th in yards allowed.
Harrison has 84.5 sacks in his 16-year career.