Saints coach Sean Payton

Two days before the scouting combine in Indianapolis kicked off in earnest, NFL Media's Mike Mayock said the Saints should select an offensive lineman with the 27th overall pick of the upcoming draft.

Mayock, draft expert for NFL Media, mentioned three names as possibilities during a Tuesday conference call with reporters: Notre Dame tackle Zack Martin (a 6-foot-4, 305-pound redshirt senior), Alabama tackle Cyrus Kouandijo (a 6-foot-5, 310-pound junior) and Stanford guard David Yankey (a 6-foot-5, 314-pound redshirt junior).

Mayock assumes the top three offensive linemen in the draft will be Texas A&M tackle Jake Matthews, Auburn tackle Greg Robinson and Michigan tackle Taylor Lewan. Martin, Kouandijo and Yankey are the fourth-, fifth- and sixth-best ranked offensive linemen, respectively, according to information supplied to by the website NFL Draft Scout.

Other tackles some think the Saints could take at No. 27 are Virginia's Morgan Moses, a 6-foot-6, 325-pound senior; and Tennessee's Antonio Richardson, a 6-foot-6, 327-pound junior. ESPN's Todd McShay has said the Saints could choose Moses, and his colleague Mel Kiper indicated that New Orleans might go with Richardson.

The predictions of Mayock, McShay and Richardson arguably make sense. Three players who started on the Saints' offensive line in 2013 -- left tackle Charles Brown, right tackle Zach Strief and center Brian de la Puente -- are set to become unrestricted free agents. Furthermore, quarterback Drew Brees in 2013 was sacked 37 times, a career high by 10. He had never been sacked in New Orleans more than 26 times.

"They've had issues there ..., and when they're good, Drew Brees can step up into a clean pocket," Mayock said. "It hasn't been quite as good. So, at 27, it's just a matter of being nimble and trying to find the best offensive lineman left."

However, the remarks of Mayock, McShay and Kiper are surprising in some respects. The Saints could also use help at other positions such as wide receiver and cornerback; they haven't drafted an offensive lineman in the first round since coach Sean Payton took over in 2006; and Brown was benched late in the campaign in favor of promising rookie Terron Armstead.

Payton and the Saints have repeatedly succeeded when plucking offensive linemen from the middle and late and late portions of the draft. Strief, a seventh-round pick in 2006, has started 42 games (including the playoffs) since 2011. Four-time First-Team All-Pro Jahri Evans was a fourth-rounder in 2006. Guard Carl Nicks, now with Tampa Bay, was All-Pro for the Saints in 2010 and 2011 after being drafted in the fifth round by New Orleans in 2008. Armstead, who settled in following the first half of his debut and played mostly well for four games, was chosen in the third round.

Nonetheless, Mayock called the 2014 draft class "the deepest, best (one) in 10 years," and he says scouts and general managers with whom he's spoken agree.

"Having a top 20 pick this year is like having a top 10 pick last year," he said, adding that starting-caliber players at all positions will be available later than usual.

Prospects invited to the combine begin their media interviews on Thursday, when their measurements will also be recorded. The Saints are one of three NFL teams not scheduled to meet with journalists in Indianapolis.

The first round of the draft will be May 8 in New York.

In discussing the Saints' first-round pick, Mayock alluded to their salary cap situation. New Orleans is reportedly just under the 2014 salary cap of $126 million after recently releasing defensive veterans Will Smith, Roman Harper and Jabari Greer.

Meanwhile, the Saints are focused on re-signing All-Pro tight end Jimmy Graham to a new long-term contract. Should that drag out, they are prepared to use the franchise tag on him if necessary to retain him through 2014.

The franchise tag window opened on Monday and expires March 3. If the Saints tag Graham, it's expected he will file a grievance with the NFL Players Association arguing that he should be considered a wide receiver.

A franchise tag is worth about $5 million more for a wide receiver than it is for a tight end. Graham spends the majority of his time on the field lined up out wide for the Saints.

Saints have fourth-most dead money: On an unrelated note, ESPN reported Tuesday that the Saints are carrying $10 million in dead money, which is the fourth-highest total among NFL teams. Dead money refers to dollars teams can't get back and owe to players who are no longer on the roster because they retired, were cut or were traded.