The 64-year-old Swede watched the Bundesliga second division outfit lose 2-0 at home to Cologne on Friday as a guest of Hamada Iraki - a representative of majority shareholder Sheikh Hasan Adbullah Ismaik.
1860 director Robert Schaefer told German newspaper Bild: "Eriksson is a good friend of Iraki, he was in Munich and used the opportunity to watch a game.
"I wouldn't rule it out that he will be the 1860 coach in the future."
Eriksson, who led England to three successive quarter-finals in major championships, is currently employed as technical director of Thai side BEC Tero Sasana, a post he took up in September.
He has had previous stints with a host of top European clubs, including Manchester City, Sampdoria, Benfica and Lazio, before being sacked as Leicester boss in October last year.
Maurer was relieved of his role after two years in charge at Munich, following a poor run which has seen them take just four points from their last six games.
Reserve team coach Alexander Schmidt has been appointed caretaker coach.