The Arizona graduate, who lives with his family in San Diego, has been contacted by the Warriors, according to the New York Daily News.
Bay Area News Group columnist Marcus Thompson II reported that Kerr is interested in the Warriors.
The Warriors are also rumored to be very interested in former Miami Heat and Orlando Magic head coach Stan Van Gundy.
"Kerr has strong relationships with Warriors owner Joe Lacob, son Kirk Lacob (who works in Golden State's front office) and Warriors president Rick Welts, with whom Kerr worked closely in Phoenix," ESPNNewYork.com reported on Tuesday.
Warriors general manager Bob Myers talked about Kerr.
"I think very highly of him as an individual, as well as a great basketball mind."
Van Gundy coached the Heat to the Eastern Conference finals in 2004-2005. He stepped down during the 2005-2006 season, handing Pat Riley a Heat team that went on to win the NBA championship.
Van Gundy, 54, led the Magic to the NBA Finals. He has a career record of 579-371. His teams reached the playoffs in each of the eight seasons he was a head coach.
Others mentioned as replacements for fired head coach Mark Jackson include Connecticut coach Kevin Ollie and Iowa State coach Fred Hoiberg. Both played in the NBA.