The visit took place two weeks ago and reportedly left the Patriots' brass "intrigued and impressed" with Jackson, per Rapoport.
Jackson, who is the 2016 Heisman Trophy winner, passed for more than 3,500 yards and ran for more than 1,500 in each of his final two college seasons before declaring early for the NFL Draft. He was measured at 6-foot-2 and 216 pounds at the Combine.
The Patriots, who own the No's. 23 and 31 picks in the first round of the 2018 NFL Draft, could be looking to improve their depth at quarterback as three-time NFL MVP Tom Brady reportedly has failed to commit for the 2018 season.
Brady, who will turn 41 in August, received NFL MVP honors for the third time in his career last season, although the lure of spending more time with family is there, sources told ESPN.
Brian Hoyer remains the only other quarterback on the Patriots' roster heading into the draft, which begins Thursday at AT&T Stadium in Arlington, Texas. Hoyer signed a three-year deal with the team after the trade deadline last season.
The last two quarterbacks the Patriots drafted -- Jacoby Brissett (2016, third round) and Jimmy Garoppolo (2014, second round) -- were traded away last season to the Indianapolis Colts and San Francisco 49ers, respectively.
The Cleveland Browns, who are coming off a 0-16 campaign, are expected to pick a high-profile quarterback with either the No. 1 or 4 selection in this year's draft.
NFLDraftScout.com senior analyst Rob Rang lists USC quarterback Sam Darnold first in his most recent Big Board. UCLA quarterback Josh Rosen, Penn State running back Saquon Barkley, Notre Dame guard Quenton Nelson and North Carolina State defensive end Bradley Chubb round out the top five.
The Patriots have depth in this draft after sending wide receiver Brandin Cooks and a 2018 fourth-round draft pick (No. 136 overall) to the Los Angeles Rams last month. New England received the 23rd overall selection in the first round of this year's draft and a sixth-round draft pick (No. 198).
The Patriots now have two first-round picks and two second-round selections in the 2018 NFL Draft, a total of four in the top 63. By comparison, they only had four picks in all of last year's draft.