Niumatalolo, though, has made a decision to stay put.
Niumatalolo later said in a statement, via the Capital Gazette: "After much prayer and pondering it has become crystal clear that USNA is a special place with special people and I love it here. Plus I have unfinished business to finish".
Niumatalolo has been extremely successful in his time at Navy. In his first 11 years with Navy, Niumatalolo took the school to bowl games in all but one season, failing to qualify for a bowl game in 2011 when the Midshipmen went just 5-7.
Niumatalolo's announcement follows a Saturday-night meeting with Navy Athletic Director Chet Gladchuk.
Arizona fired Rich Rodriguez earlier this month in the wake of a sexual harassment allegation the university began investigating in October, and a recent notice of a hostile-workplace lawsuit to be filed against Rodriguez.
Niumatalolo was considered to be a strong candidate for the opening with the Wildcats, but Sunday morning reports emerged that he was no longer in contention for the job. The former Arizona coach has admitted to having an affair. He led Navy to victories over archrival Army in each of his first eight seasons and is beloved among the fan base both for his team's performance and for his reputation as an affable, highly principled leader.