Justin Pugh, Shane Vereen practicing in preparation for Cowboys

EAST RUTHERFORD, N.J. -- While the New York Giants defense lost a key piece this week to injury, the offense could be gaining a pair of valuable parts Sunday when they host the Dallas Cowboys on Sunday night at MetLife Stadium.

Starting left guard Justin Pugh and running back Shane Vereen practiced Wednesday with hopes of returning for the key divisional matchup. Pugh has missed four games with a sprained MCL in his right knee while Vereen has been out since Week 3 with a torn triceps.

More good news: Defensive end Owa Odighizuwa and linebacker Mark Herzlich returned to practice.

The full injury rundown:

S Nat Berhe (concussion) -- He remains sidelined in the concussion protocol. Berhe has been at the Giants facility but isn’t practicing. He suffered a concussion in a Week 12 win over the Cleveland Browns. It was his second of the season. There is no timetable for his return.

DT Johnathan Hankins (quadriceps) -- The starting tackle left Sunday’s loss in Pittsburgh with the injury but did return. He was riding the stationary bike at the start of Wednesday’s practice before exiting to work with a trainer. Hankins’ injury is not believed to be serious. He seems to have a decent chance to play against the Cowboys. "I'm going to play Sunday," Hankins said. "I'm not worried about that."

WR Dwayne Harris (ankle) -- Every week it's a new injury for the wide receiver/special-teams ace. Harris left early Sunday in Pittsburgh with the ankle injury and limped to the locker room. He was also riding the stationary bike at the start of Wednesday’s practice. Harris has shown in the past he can play through pain. Don’t be surprised to see him return to practice at some point this week and play on Sunday.

LB Mark Herzlich (concussion) -- He is back after missing Sunday’s loss in Pittsburgh. It was at least his second career concussion. Herzlich was a limited participant in the non-contact portion of practice.

DE Owa Odighizuwa (knee) -- He was hoping to be a full participant in practice after missing Sunday’s loss in Pittsburgh. Instead he was limited. The Giants need Odighizuwa with Jason Pierre-Paul sidelined after surgery. Odighizuwa had a sprained MCL but has his sights set on a return this week. Practicing Wednesday in some capacity was the first step.

DE Jason Pierre-Paul (core muscle) -- He underwent surgery on Wednesday morning and is expected to be sidelined at least six weeks. He’s out for the remainder of the regular season and his only chance for a return is if the Giants make a deep run in the playoffs.

LG Justin Pugh (knee) -- He was planning to be a full participant in practice on Wednesday. He was officially listed as limited, but he insists he's feeling good and plans on playing Sunday. “Until I’m told different, I’m going to prepare as if I’m playing,” Pugh said on Tuesday. Thursday will be a big day when the Giants are likely to hold a padded practice. Pugh has missed the past four games with a sprained right MCL suffered in a win over the Philadelphia Eagles.

CB Coty Sensabaugh (ribs) -- He left Sunday’s game against the Steelers and was taken to a hospital for evaluation. Everything checked out and Sensabaugh returned with the team to New Jersey. He feels better and practiced in a limited capacity Wednesday. He's expected to be ready for the Cowboys.

RB Shane Vereen (triceps) -- He returned to practice last week after being designated for return. Vereen has been on injured reserve since Week 3. He would provide a big boost to the Giants' sluggish offense if he can return this week. Vereen is hoping it happens. He says he feels good. He’s simply waiting for the green light from the medical staff. Thursday’s potentially padded practice will be key.