Matt Rhule is leaving behind the sun to find out if his future is brighter in the NFL.

Rhule is expected to interview for the Giants’ head coach vacancy as soon as Tuesday, The Post confirmed. He emerged as the early favorite simultaneous to Pat Shurmur’s firing Monday but coached Baylor in the Sugar Bowl on Wednesday and then took a short vacation to Mexico.

Chiefs offensive coordinator Eric Bieniemy and Ravens defensive coordinator Don Martindale interviewed with the Giants on Saturday, following Cowboys defensive backs coach Kris Richard and former Packers coach Mike McCarthy coming through the door to meet with Giants co-owner John Mara and the front office.

McCarthy is the other top candidate, as The Post reported, but Rhule is the only one who has experience in the organization. The 44-year-old native New Yorker was an assistant offensive line coach under Tom Coughlin in 2012 and counts Bill Parcells as a mentor.

In 2018, Rhule interviewed with the Colts and was hoping for an audience with the Giants, according to a source close to him. It never came when Shurmur was hired from a pool of six other candidates. Rhule was a finalist for the Jets in 2019 but was never offered the job, as the two sides disagreed over who would be on his staff.

But the timing could be right to make a move, as Baylor’s 2020 recruiting class is ranked No. 4 in the 10-team Big XII Conference and No. 35 nationally by 247Sports despite a season in which it was one play away from the College Football Playoff. The Bears should be top 10-caliber again next season, but for how much longer?

There are hurdles to overcome for the Giants: Rhule’s contractual buyout from Baylor is believed to be more than $10 million and there are questions regarding who he will target as assistants given his lack of NFL experience.

After the last two coaches called plays and fell short in other aspects of the job, the Giants are seeking “leadership” above all else. Rhule showed it in rebuilding downtrodden programs at Temple and Baylor.

NFL Network reported Rhule will interview with the Panthers on Monday, before the Giants.

The Giants did not interview a college coach in either of their two searches over the past four years and have not hired a coach directly out of the NCAA since plucking Jim Lee Howell from Wagner in 1954.

Giants general manager Dave Gettleman was a senior pro personnel analyst in 2012 — not exactly a position that crosses over much with the assistant offensive line coach — but Rhule praised Gettleman as “first class” and a “football man” in a December 2017 radio interview with host Zach Gelb.

Gettleman says he is willing to cede some personnel control if Giants ownership asks.

“We are getting younger and younger players in the league,” Gettleman said earlier this week. “So, to take a college coach now, I think he would have that advantage of having been connected to these college kids for so long. Understanding the culture and what they’re at, what they’re about. I would say to anybody, any college coach that we talk to, I’m here to help him.”

Patriots offensive coordinator Josh McDaniels and Patriots special teams coordinator Joe Judge also are expected to interview this week. McDaniels reportedly has three interviews (Panthers, Browns, Giants) scheduled Friday.

One factor clouding the search is Jason Garrett’s uncertain status with the Cowboys. He has not been fired, but his contract expires Jan. 14, and the Cowboys reportedly are speaking with McCarthy and Marvin Lewis about their head coaching job.

If Garrett becomes available, he could get an interview. NFL Network reported the Giants would be his preferred landing spot, and the Giants’ brass maintained respect for Garrett — a former backup quarterback to Kerry Collins — across rivalry lines.

For more on the Giants, listen to the latest episode of the “Blue Rush” podcast: