No he wasn't involved.
Yes, Prince and Kim Basinger dated in the late 1980s, but this ended somewhere in 1990.
Basinger started recording her album after they had broken up:
Given the wisdom of hindsight, we have come to the conclusion that the 1989 relationship between Prince, 32, and Kim Basinger, 36, had less to do with romance and more to do with a calculated attempt on Basinger’s part to learn everything she could from Prince about the recording process.
Now ensconced romantically with Alec Baldwin, her co-star in Disney’s forthcoming The Marrying Man, Basinger, whose singing in the film is said to be first-rate, has just signed a recording contract with Hollywood-based Giant Records. That is the label founded earlier this year by former MCA Records chairman Irving Azoff.
Sources at Giant say they were “very impressed” with Basinger’s original material and her urban-contemporary singing style. As for her first album. Basinger is expected to enter the studio early in 1991. Don’t look for Prince to make a guest appearance on it. Sources say His Purpleness and Kim don’t speak anymore.
The album was written and produced by Robert Brookins, Gordon Jones and Timmy Gatling. Gatling was a childhood friend of Teddy Riley and was an original member of Guy, the R&B band widely credited as creators of the new jack swing style of the late 1980s and early 1990s; this connection explains the style of Basinger's album.
Considering that Prince bootlegs always were very popular, bootleggers obviously decided to exploit this when they marketed their illicit releases of Basinger's unreleased album (often titled Hollywood Affair) and linked him to the album, often including other Prince outtakes as "bonus" tracks.
The track names were also "Princefied" (e.g. replacing "too" with "2", "you" with "U") to mislead potential buyers:
- Come On
- My Love Will Find U
- I Wanna
- 2 Naughty
- Love At First Sight
- Show Me
- Action Action
- Color Of Sex
- Will U Stay With Me
The only record that involves both Prince and Kim Basinger is a maxi-single of the Batman track "Scandalous" called The Scandalous Sex Suite, which features a three part 19 minute suite of the song.