According to SNY's Ralph Vacchiano, a league source said the Giants' owners "like [Rhule] a lot" and have been enamored with him since he spent one season as an assistant offensive line coach for the Giants in 2012.
Per ESPN's Adam Schefter, the Giants are one of three teams who have requested permission to interview McDaniels.
Rhule, 44, is a New York City native who played collegiately at Penn State. After serving several years as an assistant at Temple, he spent 2012 on Tom Coughlin's staff with the Giants. Rhule then returned to Temple in 2013 to take over as head coach.
He posted a 28-23 record in four seasons at Temple before getting hired by Baylor prior to the 2017 season. Rhule went just 1-11 in his first season at Baylor but improved to 7-6 last season and 11-2 thus far in 2019.
Rhule is scheduled to lead the No. 7 Bears into the Sugar Bowl on New Year's Day against the No. 5 Georgia Bulldogs.
Just two years removed from going 1-11, Rhule was likely a win over Oklahoma in the Big 12 Championship Game away from leading Baylor to the College Football Playoff for the first time in program history.
Rhule has shown a propensity for entering bad situations and turning them around quickly. Much like Baylor, Rhule struggled early at Temple with a 2-10 record in 2013 before going 6-6 in 2014 and then winning 10 games in each of the next two seasons.
His overall record of 47-42 as a collegiate head coach doesn't leap off the page, but given how poor Temple and Baylor were when he took over, it speaks to his effectiveness as a leader.
In New York, Rhule would take the reins of a Giants team that has not made the playoffs since 2016 and has won a grand total of 12 games over the past three seasons combined.
McDaniels has some NFL head coaching experience, as he went 11-17 in parts of two seasons with the Denver Broncos from 2009-2010. He was a Patriots assistant for eight seasons before that and spent one season as offensive coordinator of the St. Louis Rams following his firing by Denver.
The 43-year-old McDaniels returned to New England in 2012 and has served as the Patriots' offensive coordinator and quarterbacks coach ever since.
Overall, McDaniels has won six Super Bowl championships as an assistant in New England, but his poor stint in Denver and the fact that he accepted and then reneged on the Indianapolis Colts' head coaching job in 2018 could make him a somewhat risky hire.
There are some exciting pieces in place on the offensive side of the ball in New York, though, which could make McDaniels an attractive option.
Rookie quarterback Daniel Jones was responsible for 26 touchdowns in 13 games and running back Saquon Barkley topped 1,000 rushing yards despite missing three games because of injury.
Also, wide receivers Sterling Shepard, Golden Tate and Darius Slayton, and tight ends Evan Engram and Kaden Smith, make up a talented group of pass-catchers.
There is work to be done on a defense that ranked 25th in yardage allowed and 30th in points allowed, but either Rhule or McDaniels wouldn't be taking over a team completely devoid of talent.