What or who is "Minami" in "Search for Minami"?
The Minami means Minami Asakura in the anime Touch.

When the anime aired, it was very very famous and everyone knew the character.
She is a heroine in the manga and she likes sports.

One daily news show called Super Time started a new corner "Search for Minami!" which finds sports girl every day and interviews them.

It's an 80's show, no one knows that now, but the author of Kare Kano likes these kinds of random jokes.