Citing sources knowledgeable about the situation, All Things Digital said Friday the talks were serious, but had not gotten to the stage of contract negotiations.
Mulally, a former CEO at Boeing Co., has been with Ford for seven years and has said recently he is "focused on serving Ford."
However, several factors suggest a switch to Microsoft is possible -- including the fact Mulally still keeps the home in Seattle he owned when he worked for Boeing and he is known to covet the idea of returning there, the report said.
Mulally was an adviser to departing Microsoft CEO Steve Ballmer concerning a recent Microsoft restructuring.
Mulally, while resistant to the idea at first, has softened on the idea of moving over to Microsoft, the sources said.
Other contenders for the job include Nokia CEO Stephen Elop. Nokia is now owned by Microsoft.
Two executives with experience at Microsoft -- Tony Bates, the former CEO of Skype, and Paul Maritz, a former Microsoft executive who is currently the CEO at Pivotal -- are also in the running for the Microsoft job, All Things Digital said.