EAST RUTHERFORD, N.J. -- The New York Giants are in the midst of a general manager search, which has put the head-coaching vacancy on the back burner. This is by design. It is the preferred route of Giants ownership after firing general manager Jerry Reese and coach Ben McAdoo earlier this month.

If the Giants have done anything in their search for a coach, it has been under-the-surface, back-channel groundwork. Maybe they’ve gauged the interest of some big-name college coaches, such as Stanford’s David Shaw or Alabama’s Nick Saban or ESPN’s Jon Gruden, just in case. More likely they have the process on hold as they attend to other business.

The Giants would prefer their new general manager have a significant role in the coaching search. So that comes first.

When it comes to hiring a coach, a lot will depend on the general manager. If it’s New England Patriots personnel guru Nick Caserio or ESPN’s Louis Riddick, the chances of Patriots offensive coordinator Josh McDaniels getting the gig rises. If it’s former Carolina Panthers GM Dave Gettleman (the early favorite), the odds that Panthers defensive coordinator Steve Wilks enters the mix increase.

Patriots offensive coordinator Josh McDaniels could be a prime fit with the Giants, who may potentially be looking to draft a quarterback early in the first round. Maddie Meyer/Getty Images

What we know about the Giants’ coaching search right now is limited.

(1) They would prefer separation between coaching and personnel. That's the way the Giants have conducted business in the past, and they'd want it that way moving forward. The coach isn’t likely to have complete power, though it depends on the situation.

“I would never say never if the right candidate was there,” co-owner John Mara said several weeks back.

(2) They’re not going to shy away from a first-time head coach because of the failings of McAdoo. Mara noted that if the franchise has the right guy, they'll go for it regardless. He's seen other young, first-time coaches succeed recently (think the Rams' Sean McVay).

(3) Mara and chairman Steve Tisch have the final say on the coaching decision. The GM has only so much power in their organizational structure.

That being said, here are some of the most likely coaching candidates who could emerge (from most likely to least) after speaking with sources in and around the Giants organization:

The favorites

Josh McDaniels, Patriots offensive coordinator

He is believed to have connections to two of the expected general manager candidates in Caserio and Riddick. He’s been a head coach in the past and would be an ideal fit for a team that might be drafting a quarterback No. 2 overall with his offensive background. Caserio and McDaniels would like to work as a package deal if the situation were right. This could be the right spot for them, especially with Patriots coach Bill Belichick’s close ties to the organization.

Steve Wilks, Panthers defensive coordinator

He’s very well-regarded as Carolina’s defensive coordinator. Wilks heads the league’s seventh-ranked defense and was the assistant head coach to Ron Rivera the previous two seasons. He also knows Gettleman quite well, as they worked together with the Panthers.

Keep an eye on (the hot assistants)

Dave Toub, Chiefs special-teams coordinator

He's going to get a legitimate opportunity to land a job in this coaching cycle after some interviews the past few years. Toub is know as a tremendous leader; he addresses the entire team on a weekly basis. He's also a New York native, which can't hurt after McAdoo's failure to connect with the fans.

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Matt Patricia, Patriots defensive coordinator

He’s unique, but his track record speaks for itself. The 43-year-old rocket scientist fixed his unit midseason, to the point that it has allowed the sixth-fewest points this year. He would be a risk but potentially one that could pay great dividends.

Matt Nagy, Chiefs offensive coordinator

He’s climbed the coaching ladder quickly and is considered a bright young offensive mind. He has a chance to win a job -- maybe even the Giants' -- with a strong interview.

Mike Vrabel, Texans defensive coordinator

His first year as a defensive coordinator didn’t exactly go as planned, in part because Houston was ravaged by injuries. Vrabel is still considered a strong option given his ability to lead.

Others: Steelers offensive coordinator Todd Haley; Vikings offensive coordinator Pat Shurmur; Eagles quarterbacks coach John DeFilippo; Seahawks defensive coordinator Kris Richards

Outside the box, but ... maybe

Brian Kelly, Notre Dame coach

His name has been linked to NFL jobs before, and the Giants have some ties to Notre Dame. The organizational structure might make this tough, as Kelly is known as a control freak. Don’t rule it out completely, though.

Jim Harbaugh, Michigan coach

A return to the NFL seems inevitable at some point. Why not with a new young quarterback to mentor and weapons such as Odell Beckham Jr., Sterling Shepard and Evan Engram? This might intrigue Harbaugh if the Giants reach out.

Long, long, long shots

Jon Gruden, ESPN analyst

He might not be an ideal fit with the Giants, but there is a more chatter this year that he could leave the booth (more likely for Tampa Bay) than usual.

Nick Saban, Alabama coach

You can never completely count him out when it comes to the Giants. They have been interested in the past.

David Shaw, Stanford coach

He would be among the targets if he were to be interested in making the jump. It once again doesn't appear he's interested.