It seems like there's two potential connections that stand out, May Manning or David Morris.
May is the oldest of Cooper's three kids, and she graduates from high school this spring. Based off no real evidence, the pick could be UT. I didn't really dig too far into this for obvious reasons. This could be a big connection, but it doesn't feel like a "pretty fucking big" connection.
David Morris was Eli's backup at Ole Miss for four years. He founded a quarterback training and development company called QB Country. Steve Sarkisian currently follows the QB Country twitter account (I couldn't find any personal twitter account for David Morris). The NY Times reported that "since he was in junior high school, Arch Manning has worked at times with a quarterback coach named David Morris" in the following article: https://www.nytimes.com/2020/11/26/sports/football/arch-manning-high-school-recruitment.html . According to Morris's bio on the QB Country website ( https://qbcountry.com/mobile-al/ ), he trained Eli in his offseasons. So there's a good connection there with Arch and the Manning family, but in order to make it a "pretty fucking big one" maybe Morris will be offered a position at UT?