The Giants are searching for 37 receptions from their most productive tight end this season.

That number is flexible, but something in that neighborhood would be a significant boost for the offense. From 2008-2011, the Giants' top receiving tight end averaged 37 catches a season. That included highs of 42 receptions by Kevin Boss in 2010 and 38 by Jake Ballard in the 2011 championship season. Ballard yesterday was waived/failed physical, a transaction stemming from the torn anterior cruciate ligament he suffered in Super Bowl XLVI.

So now the Giants are looking for a tight end who can become a reliable target for Eli Manning in 2012. The steady and dependable Bear Pascoe is still here, the team signed free agent Martellus Bennett, incumbent Travis Beckum is rehabbing his own torn ACL, and fourth-round draft choice Adrien Robinson is finally here after missing most of the spring work while completing his academic requirements at the University of Cincinnati.

"We do have some athletes there and some guys we hope are going to be able to really come through for us," coach Tom Coughlin said at the start of the three-day mandatory minicamp that began today. "I think Travis Beckum will be back at some point in time. We have a lot of young guys that have a tremendous amount of learning to do. Some days it looks good and other days not so good. So this is something that is very important, very much needed. And so we continue with this process."

Beckum, who said he also had cartilage damage in his knee, has been working out and will run today for the first time. Coughlin said it is "reasonable" to believe Beckum will return, perhaps for the start of the season.

"He has done very well," Coughlin said. "But again, I'm not a doctor. He has not even run yet.  So maybe I'm being a little too optimistic here."

Beckum is taking a cautious approach and is refraining from predictions.

"I'm kind of taking it week-by-week, day-by-day, and whatever my knee tells me, I'm going to do," Beckum said. "So if that's PUP (the physically unable to perform list) or training camp, I'm going to go for it.

"I've done everything except running. Been in the pool a lot, been sprinting in the pool, a lot of trying to make my glutes strong, my hamstrings, my quads, so all that stuff has a factor in how my knee will hold up."

Bennett has been slowed by a sore hamstring, but Coughlin is hopeful he will participate in the camp.

"He says he is going to try to go," Coughlin said. "I would say he is probably 50-50 on what he can participate in. We will try to keep him a little bit under control so that he doesn't get into that sore mode where he can't do anything."

Robinson is in catch-up mode.

"He is back and he is ready to practice," Coughlin said. "He has a lot of meeting time to make up.  So we are trying to do that as well."

Ballard tweeted yesterday that he believes he will play for the Giants in 2013. Coughlin said Ballard's rehab is not unusually complicated.

"It wasn't any worse than what was expected – what he had was upfront from the time the surgery was done," Coughlin said. "So that is where that is."

*Coughlin said the re-signing of defensive tackle Rocky Bernard, announced yesterday, has nothing to do with Shaun Rogers' inability to work in the camp.

"(Bernard is a) good football player that helps us in a lot of different ways; solid, solid guy – great in the classroom, great with his teammates," Coughlin said. "You know one of the first guys that I saw come off that sideline when we won the Super Bowl was Rocky Bernard.  He is a good, solid football player. We know exactly what we can get out of him. He is in excellent shape.  His weight is outstanding.  So you can't have enough quality football players."

*When the minicamp concludes, the Giants will scatter until training camp.

"The message right now is 'Improvement.'" Coughlin said. "Improve on a daily basis, recognize the mission, and understand how important this little phase is right here. And then we will have a solid message for them because I do feel it is a much different five weeks between now and when we go to camp.  And maybe perhaps we have had another time before of the shortness of the current offseason program. There is some work that has to be accomplished in the offseason.  And we certainly don't want to go through these hamstrings that we have had here when we started this offseason program."