Baylor coach Matt Rhule, seen here during the Sugar Bowl...

Baylor coach Matt Rhule, seen here during the Sugar Bowl on Jan. 1, 2020 in New Orleans, will interview with the Giants on Tuesday.  Credit: Getty Images/Sean Gardner

The Giants hit the road in search of a new head coach on Saturday, but the candidate many consider to be the favorite will visit them in New Jersey early this week.

Baylor head coach Matt Rhule is expected to meet with the Giants on Tuesday. A source confirmed the timing of the interview, which was first reported by the NFL Network.

Rhule, who has been vacationing with his family since his team lost in the Sugar Bowl on Wednesday, is scheduled to meet with the Panthers about their vacancy at head coach on Monday. That creates the possibility that the Panthers could hire Rhule before he gets a chance to meet with the Giants. However, it’s widely believed that Rhule has had his eye on the Giants’ job for a while and that it might be the only one for which he would consider leaving Baylor.

If the interview with Rhule goes well this week, the Giants’ search could wrap up quickly — perhaps even before they meet with Patriots offensive coordinator Josh McDaniels (whom they interviewed for the opening two years ago) and special teams coordinator Joe Judge. Those interviews are penciled in for Friday.

Rhule, who was a well-regarded assistant offensive line coach with the Giants in 2012, has been a head coach with Temple and Baylor in the college ranks, lifting both programs from afterthoughts to prominence.

He was a finalist for the Jets’ opening a year ago but removed himself from consideration because they wanted to dictate the makeup of his staff. The Giants have a long-held philosophy of allowing head coaches to hire their own staff, so while they may have suggestions — especially when it comes to an offensive coordinator to handle the development of quarterback Daniel Jones — that sort of roadblock is unlikely.

Rhule has what the Giants seem to be looking for in their next head coach, with experience on both sides of the line of scrimmage but no defined area that he would run. He would be the coach of the Giants, not the coach of the Giants’ offense or defense. The last two hires as head coach for the Giants were offensive play-callers whose attention slanted toward that side of the ball.

“I really believe that the head coach position is a CEO position,” general manager Dave Gettleman said in a radio interview this past week. “In this day and age, you think of all the different tentacles of a football operation, he’s got to be CEO-smart, intelligent. He’s got to be focused. And of course he has to be a leader. One of the things that makes football unique is the number of people involved in getting it right. There’s got to be leadership.”

Co-owner John Mara, Gettleman and vice president of football operations Kevin Abrams traveled to Kansas City to interview Chiefs offensive coordinator Eric Bieniemy on Saturday morning and then dashed off to Baltimore to meet with Ravens defensive coordinator Don “Wink” Martindale. Their teams are on a bye from the playoffs this weekend. If the Giants want to hire either of them, it could mean waiting as long as until after the Super Bowl.

They were the third and fourth candidates to interview for the opening created when Pat Shurmur was fired last Monday. Mike McCarthy, who interviewed with the Giants on Friday, met with the Cowboys on Saturday. The Giants also interviewed Cowboys assistant coach Kris Richard last week.

How many interviews the Giants have in total may depend on how well the fifth one goes.

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