The best standard for a close-grip bench press is to set your hands so that your arms are perfectly parallel while extended. This is difficult to see on your own, so filming yourself or enlisting some help may be necessary.
Be prepared to use less weight for a CGBP than a conventional bench press because this closer hand position makes things more challenging. The bar travels a little further, and your chest isn’t able to contribute quite as much, which leaves extra work for your triceps.
For some trainees, this closer grip may cause discomfort through the wrists or shoulders. If this applies to you, don’t force it. Just move your hands wider bit by bit until the exercise feels comfortable. Once you find the right spot, note where your hands are in relation to the knurl marks on the barbell so you can easily find your grip for future sets.
If you happen to be thinking: “I thought close-grip meant closer than shoulder-width”, you’re correct. For other exercises like rows, we use ‘mid’ to denote a shoulder-width grip, but the CGBP is the outlier here. It’s confusing, I know, but I guess the people who first named these exercises just never thought to consult one another.