The Dolphins have had multiple conversations with Harbaugh about the position, according to a league source.
Harbaugh will begin exploring his coaching options now with Stanford's season complete, and the process is not expected to take long. The University of Michigan, San Francisco 49ers and Denver Broncos are among the teams that want him, but the Dolphins are quietly evaluating him as well, according to sources.
Dolphins owner Stephen Ross, along with close friend and adviser Carl Peterson, was at the Orange Bowl Monday night, where Harbaugh coached fifth-ranked Stanford to a convincing 40-12 victory over No. 12 Virginia Tech in the Orange Bowl.
The Dolphins have yet to make any statement on Tony Sparano's future. However, an NFL source told NFL.com senior writer Steve Wyche that it will be "hard for Sparano to survive" with the Dolphins. The question now is more about general manager Jeff Ireland's status.
Sparano, who has directed the Dolphins to consecutive 7-9 records after an 11-5 mark in 2008, met with Ross on Monday. Behind the scenes, the Dolphins are trying to determine if they can land a higher profile coach who might be a better fit and play more attractive offensive football.
Harbaugh fits that description and, unlike some other big-name candidates, would not need to bring his own personnel people with him. Harbaugh has some ties to Ireland and likely would be more willing to work with him than he would be some of the less-established entities in the front office in Denver and San Francisco.
Harbaugh also could work with Miami defensive coordinator Mike Nolan, whose unit is coming off a strong performance there.
The Dolphins have not been linked prominently with Harbaugh but there is reason to believe this could come together.
Furthermore, Sparano has been given no timetable as to when a decision on his future with the Dolphins will be made following his talks with ownership and management, according to a source with knowledge of the situation.
"That's open-ended right now," the source said.
Harbaugh spent the past week in South Florida as Stanford prepared for the Orange Bowl and has been approached by the Dolphins, according to the source.
It is also worth noting that Ross, who attended the Orange Bowl, is a huge donor to Michigan and like Harbaugh is a Michigan graduate. He is well aware of Harbaugh's accomplishments in football on the field and as a coach.