If you are looking to transfer an image from Photoshop to Illustrator without using a white background, there are a few things you can do. First, make sure that the image is in RGB color space. Second, make sure that the image is at least 2048px wide. Third, make sure that the image has a resolution of at least 72 dpi. Finally, use the Image > Save As command to save the image as a PDF or JPEG file.