Todd McShay says the Giants' selection of Saquon Barkley shows that they want to return to the physical, Big Blue style of offense. (1:11)

EAST RUTHERFORD, N.J. -- The New York Giants never flinched when Penn State running back Saquon Barkley was on the board for the No. 2 overall pick. They didn’t even listen to offers once they were officially on the clock.

The Giants wanted Barkley. They got their guy.

As the draft resets Friday night for Day 2, which features the second and third rounds, the Giants might be in a similar situation with their next selection. They own the second pick of the second round (No. 34 overall).

The way it usually works at the top of the second round is teams have a chance to grab players whom they had given first-round grades. It’s what happened in the 2015 draft when the Giants traded to pick No. 33 and selected safety Landon Collins out of Alabama. They were surprised Collins was available. They viewed him as a first-round player. So they went and made him their pick, even if it meant trading up to do so.

Will Hernandez is a physical guard who fits the Giants' needs for their offensive line. Joe Robbins/Getty Images

The Giants don’t need to trade up this time. But there are some players on the board who almost certainly had first-round grades from general manager Dave Gettleman and his staff. The most notable is UTEP guard Will Hernandez. He’s this year's heavy favorite to be the Giants’ second-round selection, No. 34 overall.

Some options for the Giants’ Day 2 picks (No. 34, 66 and 69):

Second Round (No. 34):

G Will Hernandez (UTEP): The heavy favorite. The Giants are lucky he fell into their lap. Hernandez is the mauling guard that Gettleman desires. He doesn’t have ideal height (6-2) and measurables. That is believed to be why he fell. But Hernandez is physical, a good run blocker and “really good,” according to multiple scouts. He fits perfectly with what the Giants are trying to do with their offensive rebuild.

G Austin Corbett (Nevada): If it’s not Hernandez, Corbett is a strong fallback option. A college left tackle who projects to guard, he was a productive player at the collegiate level. He’s smart, competitive and a blue-collar grinder.

C James Daniels (Iowa): Another player with a first-round grade. He’s athletic, smart and plays with balance. Just a good, solid player. Fits the mandate to fix the culture and locker room.

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OL Connor Williams (Texas): Played tackle for the Longhorns. Projects as a guard for some at the NFL level. His 2016 tape is strong. Not so much last year. He makes sense because he fits the Gettleman mold with his physical attributes and his ability as a run blocker.

CB Isaiah Oliver (Colorado): A first-round prospect for more than a few teams. His length and man-coverage ability make him a fit for the Giants, who desperately need to add talent at the cornerback position in this draft.

CB Josh Jackson (Iowa): A play-making cornerback who surprisingly dropped into the second round. Being a one-year starter and posting disappointing running times at the combine and his pro day likely scared off some teams.

CB Donte Jackson (LSU): One of the fastest players in the draft. He ran the 40-yard dash in 4.32 seconds at the NFL scouting combine. Jackson could fill a void as the Giants’ nickel cornerback.

Third Round (Nos. 66 and 69)

CB Carlton Davis (Auburn): A solid press corner with good size for the position.

CB M.J. Stewart (North Carolina): Another physical corner. Not a blazer but knows how to play the position and could be a weapon in James Bettcher’s aggressive defense.

OT Joe Noteboon (TCU): Not the ideal run blocker for right tackle, but he can pass protect.

OT Orlando Brown (Oklahoma): He is the ideal run blocker for right tackle. Might be a better fit for Gettleman.

DL R.J. McIntosh (Miami): Quick-twitch lineman who gets upfield. Would work well in Bettcher’s attacking schemes.

Edge Ogbonnia Okoronkwo (Oklahoma): May be a man without a true position but he can rush the passer. The Giants need some of those guys.