Yes, our solar system is gradually moving toward the supermassive black hole at the center of the Milky Way galaxy, known as Sagittarius A*. However, the term "sucked in" might be misleading. The motion is more about the gravitational influence of the black hole and the overall dynamics of the galaxy.
The solar system orbits the center of the Milky Way, completing one orbit approximately every 230 million years. While it is true that we are moving closer to the center, this movement is part of a stable orbit rather than a direct trajectory toward the black hole. The vast distances and the nature of gravitational forces mean that while the solar system is indeed in motion relative to the black hole, it is not in immediate danger of being "sucked in."
Additionally, the region around the black hole is complex, and many stars orbit it at varying distances and speeds. The gravitational pull of the black hole influences these motions, but it does not mean that they are being drawn into it directly. Over long periods, several galactic processes could alter the orbits of stars and systems, but these changes occur over millions of years.