Sanchez has spent the 2019-20 campaign on loan at Inter Milan but has struggled to make his mark at San Siro and is expected to head back to Old Trafford this summer.
The 31-year-old is thought to be surplus to requirements at his parent club, though, leading to suggestions that he could be moved on for good during this summer's transfer window.
According to Navarrete, Sanchez "wants to retire" at the Chilean outfit, who have won their domestic league on 18 occasions.
"I spoke with Alexis Sanchez and he is a fan of Universidad de Chile. He wants to retire by playing for the club. I would like to have Marcelo Diaz, [Mauricio] Isla, Edu (Eduardo) Vargas, Alexis Sanchez, all of them, but you have to be realistic," Navarrete told DirecTV.
"The economic scenario is not brilliant, it will depend on how much they are willing to give up to come to Universidad De Chile."
Sanchez, who is thought to be on in excess of £400,000 a week at Old Trafford, has only scored five times in 45 appearances for the 20-time English champions in all competitions.