According to David Haugh of 670 The Score, Kelly has emerged as a "coach of interest" for the Bucs.
Tampa Bay is looking to hire a new head coach after firing Dirk Koetter on Monday on the heels of a 19-29 record in three seasons at the helm.
Kelly led Notre Dame to a 12-0 record during the 2018 regular season and a berth in the College Football Playoff.
The Fighting Irish's season came to an end in the Cotton Bowl when they were decimated 30-3 by the Clemson Tigers.
Kelly is 81-35 in nine seasons at Notre Dame and 134-57 overall as a college head coach when taking into account his stints at Central Michigan and Cincinnati.
While Kelly has been linked to the NFL often in recent years, he hasn't expressed much outward interest in making the leap aside from an interview with the Philadelphia Eagles in 2013.
Despite that, Haugh reported that sources believe Kelly is "intrigued" by the idea of going to the NFL.
Haugh also reported that Glazer family, which owns the Bucs, is considering paying the organization's next head coach as much as $10 million per season, which dwarfs the $2.1 million per season Kelly is set to make at Notre Dame through 2021.
Kelly would also likely be put in charge of football operations and given full control over the roster if hired by the Bucs.
Tampa Bay has just one winning season over the past eight campaigns, and it hasn't reached the playoffs since 2007, which is the second-longest active drought in the NFL behind only the Cleveland Browns' 16-year playoff absence.
Whoever the Buccaneers hire as head coach will need to commit to Jameis Winston as the starting quarterback, based on comments made by general manager Jason Licht this week.
Kelly helped develop the unheralded Ian Book into a star under center this past season, and if given the opportunity to work with a former No. 1 overall pick, Kelly could potentially work wonders with Winston.