Allegretti's father and two uncles played football at Butler University. Nick got the call from Big Ten schools, though, after earning top-10 center recruit grades nationally. The consensus first-team All-Illinois selection and four-year wrestler redshirted his first year with the Illini. Allegretti contributed as a reserve offensive lineman in 12 games and also on the defensive line in two of those games. He stayed on offense the next season, starting once at center and the other 11 contests at guard. Allegretti was voted honorable mention All-Big Ten and was a team captain in 2017, starting all 12 games, again splitting time between center (four) and guard (eight). He was an honorable mention all-conference pick in 2018, as well, starting 12 games at guard.