FootballScoop's John Brice was the first to report LSU's interest.
Kelly, 60, is 92–39 in 12 seasons at Notre Dame. The Fighting Irish reached the College Football Playoff in 2018 and 2020 under Kelly, and they've won at least 10 games in each of the last five years.
Sources have told Sports Illustrated's Pat Forde that LSU has been "trying to make it happen" with Kelly, though there has been no confirmation Kelly has reciprocated that interest.
LSU is looking for a new head coach after announcing the firing of Ed Orgeron in October. Both Florida and USC have filled their coaching vacancies since the end of the regular season, with the Gators hiring Louisiana's Billy Napier before USC lured Riley away from Oklahoma.
Notre Dame is 11–1 in 2021 as it seeks another berth in the College Football Playoff. LSU advanced to 6–6 last week with a home win over Texas A&M to send off former coach Ed Orgeron with a win.
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