Petersen, a native of Yuba City, Calif., has a 61-5 record in five seasons at Boise, leading the Broncos to two Fiesta Bowl victories and first place in the WAC four times.
With Harbaugh taking over as coach of the San Francisco 49ers, the Cardinal also plan to look at internal candidates.
Stanford athletic director Bob Bowlsby wants to interview three current members of Harbaugh's Cardinal staff: assistant head coach Greg Roman, offensive coordinator David Shaw and defensive coordinator Vic Fangio, an athletic department source told ESPN.com's Ivan Maisel.
ESPN NFL Insider Adam Schefter has reported Fangio may join Harbaugh with the 49ers.
Bowlsby has met with the entire Orange Bowl-winning Cardinal football staff since Harbaugh's departure to first determine who the internal candidates might be.
Bowlsby said Saturday he has spoken with each member of the staff but wouldn't categorize any of the sessions as formal interviews.
"I've talked to the whole coaching staff a number of times over the last day," Bowlsby said.
Bowlsby would like the continuity an in-house hire would bring, the source told Maisel, and will interview them as soon as possible but also intends to speak with candidates outside the program.
President John Hennessy says the school would like to work quickly but also find the right person.
"We're going to get it done quickly because obviously it's important for the team," Hennessy said. "But getting the right person is the most important thing. We'll take the time we need."
Bowlsby's strategy to look at Harbaugh's staff may stem in part from quarterback Andrew Luck's decision to return to school.
Luck, the Heisman Trophy runner-up, chose to give up a likely No. 1 overall selection in this year's NFL draft to return for his junior season after leading the Cardinal to a 12-1 mark that included a 40-12 Orange Bowl victory over Virginia Tech.
Information from The Associated Press was used in this report.