In his predraft press conference, Nick Caserio, the director of player personnel for the New England Patriots, said his team was in pretty good shape.

“If you look at our team, just where we are today,’’ he said, “if we had to go out there and play a game, we feel we could field a competitive team.’’

And therein lies the rub: Patriots fans expect more than just a competitive team. They want a team that will contend for a Super Bowl championship.

Yes, the Patriots have made some big moves this offseason, signing free-agent cornerbacks Darrelle Revis and Brandon Browner and receiver Brandon LaFell and re-signing wide receiver Julian Edelman.

But the Patriots are not a complete team yet. They’ll look to fill some holes in the NFL draft, most specifically at tight end and defensive line.

Tight end is too valuable a position to Tom Brady and the Patriots’ offense for it to languish as it did last season when Rob Gronkowski was out injured.

And while they addressed their secondary through free agency, they need to address the defensive line in the draft. The Patriots need someone who can come in and make an immediate impact for a run defense that ranked 30th in the NFL last year. They need someone who can be a run stopper and get pressure up the middle.

They could use help at linebacker, where Brandon Spikes and Dane Fletcher left via free agency, and on the offensive line, which didn’t perform up to its capabilities last year. LeGarrette Blount’s loss means they have a hole in the backfield. They could always use another receiver. And, yeah, they need to start thinking about a long-term replacement for Tom Brady. He’ll turn 37 during training camp this summer.

But if the Patriots are going to challenge for another Super Bowl title this season, they need to address the tight end and defensive line positions immediately.

Tight end has become an integral position in the Patriots’ offense. New England likes to use two tight-end formations, sometimes splitting both out wide. This creates match-up nightmares for defenses, which Brady has been able to exploit.

That all changed last year when Aaron Hernandez was arrested and charged with murder in the offseason and Gronkowski missed most of the season with injuries. The two had combined for 169 catches and 24 touchdowns in 2011, 106 catches and 16 touchdowns in 2012.

Gronkowski, Michael Hoomanawanui and D.J. Williams remain on the roster. But Gronkowski is still recovering from his knee injury and no one knows when he’ll be ready. For the Patriots’ offense to be productive again, they need to get a tight end who can open up the field.

There are several in the draft. Unless they’re willing to trade up, the Patriots won’t have a shot at North Carolina’s Eric Ebron, rated as the best in the draft.

That will leave Jace Amaro of Texas Tech, Austin Seferian-Jenkins (good receiver/blocker) of Washington, Troy Niklas (big-play receiver) of Notre Dame and C.J. Fiedorowicz (blocker/receiver) of Iowa. Niklas and Fiedorowicz are more likely to fall to the Patriots, possibly into the third round. Any of them would be a huge upgrade in terms of the passing game.

The Patriots have 12 defensive linemen on their roster. But other than defensive ends Rob Ninkovich and Chandler Jones, who combined for 19.5 sacks and 40 quarterback hits last year, most are question marks. Tackles Vince Wilfork, 32, and Tommy Kelly, 33, are coming off devastating injuries – Wilfork an Achilles tear, Kelly a blown knee. Armond Armstead was brought in last year from Canada to bolster the interior line but missed the season with an undisclosed illness. Joe Vellano, Chris Jones and Marcus Forston need more experience.

Four names have popped up constantly when the “experts’’ talk about the Patriots first pick: defensive tackle Ra’Shede Hageman of Minnesota, defensive tackle Dominique Easley of Florida and Louis Nix III and Stephon Tuitt of Notre Dame. All are versatile, athletic, disruptive. Hageman lacked consistency in college, which the Patriots could see as a problem. Tuitt plays well against the run. Easley (ACL) and Nix (torn pectoral) have injury concerns. But both have potential. And remember, Coach Bill Belichick has never shied away from drafting players coming off injuries.

If the Patriots are looking at defensive ends, the intriguing ones could be Kony Ealy of Missouri and Demarcus Lawrence of Boise State.

The Patriots have the 29th pick in the first round. Maybe. They’ve made a living of trading down in recent years. Last year, in fact, they traded a 29th pick to Minnesota for four in lower rounds. That enabled the Patriots to select linebacker Jamie Collins, cornerback Logan Ryan and receiver Josh Boyce – all expected to be key contributors this year.

Should the Patriots keep the 29th pick, they could address their interior offensive line early in the draft and the defensive line in the middle or late rounds. UCLA’s Xavier Su’a-Filo could be a good fit, same with Nevada’s Joel Bitonio. Both played tackle in college, but might be better suited at guard.

Look for Saturday to be a busy day, when the Patriots have five picks in the last four rounds. They can address a lot of positions there: running back, defensive back, wide receiver, quarterback.

The Patriots have a history of selecting the best player available on their draft board, regardless of position. Caserio noted as such when he was asked if the team would draft a wide receiver after taking two in 2013. “I think what you don’t want to do is pass on a good football player regardless of your circumstance,’’ he said.

You can count on there being some surprises during the draft, not only from the Patriots but every team. And Caserio said that’s normal.

“You try to make your best guess of what you anticipate a team may or may not do,’’ he said. “But I’d say there’s probably a lot of noise out there and nobody really knows until the actual draft starts and the team picks.’’

Let the clock begin.

Mike Lowe can be reached at 791-6422 or at:mlowe@pressherald.com

Twitter: MikeLowePPH