The prominent six-floor building is located at 5300 Stevens Creek Blvd, just two miles from Apple Park, and the company has reportedly leased all 86,000-square feet of the property.
According to the report, a "considerable" amount of construction work is already to be underway on all six floors, and Apple logos can be seen throughout the building.
Apple first rented part of the building in 2012, but information from property listing services obtained by The Mercury News suggests that the company has not continuously made use of the office space.
The report notes that Apple began expanding its presence around Apple Park last year, when it leased office space in a complex located directly across from the Triangle Building.
Apple owns and leases several properties in and around the Bay Area, including its Cupertino campus in Santa Clara and offices in San Jose.