The Giants have not had a pick inside the top 10 since 2004, when they turned the No. 4 overall pick into a trade with the San Diego Chargers to get quarterback Eli Manning. That, of course, helped the Giants win two Super Bowls.
There is really one one foreseeable scenario in which the Giants could create a bidding war for the No. 9 pick, and it once again involves quarterbacks. If one of the top two quarterbacks in the 2015 draft class, Jameis Winston or Marcus Mariota, somehow falls to the Giants at No. 9 Reese would be in position to engineer a bidding war for the ninth pick.
Any such bidding war would likely include the St. Louis Rams, who have the 10th pick, and the Cleveland Browns, who have the 12th and 19th picks. Both are thought to be in the market for a quarterback. If it is Mariota who falls to No. 9 the Philadelphia Eagles could also be in the mix. Eagles coach Chip Kelly is known to covet Mariota. Philadelphia has the 20th overall selection in the first round.
It seems unlikely that the Giants would be able to move up from the ninth spot. They have an extra seventh-round pick, thanks to trading Brandon McManus to the Denver Broncos, but not much else to offer without leaving themselves without at least one mid-round pick.