The former Leicester and England hooker penned a five-year extension at Welford Road last weekend.
Cockerill, 42, had been linked with taking over at French side Clermont Auvergne during the summer.
"There has been interest from other places," he told BBC Sport. "But for me it's about security for myself and my family.
"I talk about loyalty the whole time to players and other coaches and staff here. It's all right for me to preach that but it's important that I practice that as well."
Cockerill, who took charge of the Tigers in 2009, has guided the side to three league titles.