PNG from Photoshop to Illustrator not transparent

I made an cutout of a glass cup and saucer transparent. In photoshop when I change the bakground I can see that the glass is tansparent but when I export it as a PNG and import it to Illustrator the transparency of the glass goes away. 

This is the image exported through Photoshop. As you can see the blue background here can be seen through the glass.

This is the image exported through Illustrator. Here it's not showing.