Fans are convinced that Nicks, 77, and Buckingham, 75, are teasing a new project — 52 years after their album came out and seven years after the latter parted from Fleetwood Mac.

Now, in addition to new vinyl, it will be available on streaming and CD for the first time when it’s reissued Sept. 19 on Rhino, Warner Music Group announced Wednesday.

Buckingham Nicks (Rhino High Fidelity) is limited to 5,000 copies, with a special edition of 2,000 copies that includes a replica of two 7-inch singles: “Crying in the Night” b/w “Stephanie,” and “Do...