"Buzz has surfaced about the Giants having a trade partner. While it is not certain the Jaguars are that team, Jason La Canfora of CBS Sports tweets several GMs have pointed to the Giants moving down from No. 4 and the Jags climbing up from No. 8. The Giants are believed to be serious about wanting to move down. Although the Jaguars are believed to be planning to give Gardner Minshew a legitimate opportunity, JLC speculates a move up would be for a quarterback."

Via Profootballrumors.com (they obviously have the pick wrong, it's #9, not #8).

I would be disappointed to see us move up for a QB. If they really want to give Minshew a shot this would not be a very supportive move. On top of that the team just isn't likely to win a lot of games. I'm not sure what the over/under is but I'd guess around 5.5 and I'm taking the under. If we move up it needs to be for a) Simmons, b) Brown, or c) the best one of the tackles on the board.