Travis Beckum is recovering from a torn ACL he suffered during Super Bowl XLVI, and Jake Ballard was claimed off waivers by the New England Patriots, so neither is an option.
Bear Pascoe is a backup and more of a blocking-type tight end.
Then there are the two newest additions to the Giants: free agent Martellus Bennett from the Cowboys, and Adrien Robinson, the Giants' fourth-round draft pick.
Bennett is penciled in right now as the starter, but can he keep the job long-term?
My gut says no and that Robinson will eventually take over the starting job.
I see a lot of potential in Robinson as the Giants' tight end, and I think he could eventually play a big part in the Giants' offense.
Here are five reasons why I can see Robinson taking over the starting job in 2012.
With the Cowboys, Martellus Bennett played second fiddle to Jason Witten.
Bennett was more of the blocking tight end while Witten was one of Tony Romo's favorite targets downfield.
Bennett's best season was his rookie year in 2008, catching 20 balls for 283 yards and four touchdowns. The 25-year old tight end bolted from Dallas to get a chance to start, which he wasn't going to get in Dallas.
Since he's no sure thing to be a good starting tight end, the Cowboys weren't exactly working to keep Bennett around.
Which is exactly why the Giants only signed him to a one-year deal, just in case he turns out to be a bust in New York.
Rob Gronkowski is a big reason why the tight end position is a major key to an NFL offense. In 2011, he caught 90 passes for 1,327 yards and 17 touchdowns for the Patriots.
The same can be said for Jimmy Graham of the New Orleans Saints, as he hauled in 99 passes for 1,310 yards and 11 touchdowns last year.
What made both Gronk and Graham so successful?
Their height, size and athleticism on the field.
Gronkowski is a 6'6", 265-pound animal who couldn't be covered by linebackers or defensive backs. Subsequently, he created such a huge mismatch when he was on the field.
Graham, who is also 6'6" and 260 pounds, is another athletic beast like Gronkowski who creates mismatches.
Robinson is 6'4" and 264 pounds, and he has the makings of having that kind of ability because of his size and talent.
Since taking over as the full-time starting quarterback, Eli Manning uses the tight end in his offense.
Whether it be Jeremy Shockey, Kevin Boss, Michael Matthews, Travis Beckum, Bear Pascoe or Jake Ballard, Manning found ways to get them the ball.
Now, it'll be Martellus Bennett and Adrien Robinson's turns to get involved in the offense.
Last year, we all wondered how they would replace the production voided by Boss' departure to the Oakland Raiders, and they got it with Ballard.
Ballard was turning into a solid player for the Giants until injuries derailed his season. But no matter who is the starting tight end, Eli uses them in the offense.
And if Giants offensive coordinator Kevin Gilbride finds a way to work in Robinson during his rookie season, they can catch defenses off guard by mixing him in.
Even if they run two-tight-end sets on the goal line, Manning could use Robinson as a goal-line option by using play-action to get defenders to bite on the run.
OK, so we know some of the Giants' coaching staff.
Tom Coughlin is the head coach.
Kevin Gilbride is the offensive coordinator.
Perry Fewell is the defensive coordinator.
Pat Flaherty is the offensive line coach, and one of the best line caches in the league.
Then there is Mike Pope, whom the die-hard Giant fans might know.
But for the causal fans who don't, he's the Giants' tight end coach and has been since 2000, mostly because he is also one of the best position coaches in the league.
When Coughlin took over the Giants' coaching job in 2004, Pope was the one coach Coughlin retained because of how well he can develop players at the position.
Jeremy Shockey, Kevin Boss and Jake Ballard's success can all be attributed to Pope's coaching abilities.
With Adrien Robinson's talent mixed in with Pope's coaching ability, the Giants have the making of a future star at the position.
After drafting Adrien Robinson late in the fourth round of the 2012 NFL draft, Giants general manager Jerry Reese made a pretty bold statement.
Koch said that he felt Robinson didn't start to come on until late in the season after the West Virginia game, although his numbers don't shout success.
But Reese is one of the best talent evaluators in the league and has a sixth sense for finding talent where nobody is looking.
Heck, everyone criticized Reese for drafting Jason Pierre-Paul in the first round of the 2010 NFL draft, and look how stupid we all felt for doing so when JPP turned into a superstar in 2011.
If Reese believes in this guy and feels that he has that much talent and that much upside, maybe everyone should believe Reese.
There's a little saying that's known with Giants fans: "In Reese we trust."
He got it right with JPP.
Reese isn't known for making mistakes when drafting players, and I think he's going to get it right with Adrien Robinson, which is why I think he will eventually become the starting tight end for the New York Giants.