Is it possible to change my bike standard headset to a internal headset?
The head tube of the bike has to be designed to specific dimensions to seat a specific type of headset cup. Hence, if your head tube isn’t designed for an internal headset, you can’t simply fit an internal headset to the frame. It is completely impractical to change the head tube. It may be possible in theory, but definitely not economical, because you’d have to cut out or de-bond the head tube from the rest of the frame, attach a new one, then repaint, and you would need a new fork as well since forks are designed to mate with different headset types. And you’d want to repaint the bike. If it were an aluminum bike, you’d need to heat treat the frame.
Why do you want an internal headset anyway? If the answer is to lower your stack height, then you could experiment with a stem with a lower angle (e.g. find a -17 degree stem). Presumably you would have already tried removing headset spacers. Unfortunately, this may only get you so far. If this is your problem, it would still be more economical to sell the bike and buy one that fits rather than to try to replace the head tube.