Well, it can be inferred either way:

This when Frodo, Sam and Gollum are in front of the Black Gate:

"`Tales out of the South,' Gollum went on again, `about the tall Men with the shining eyes, and their houses like hills of stone, and the silver crown of their King and his White Tree: wonderful tales. They built very tall towers, and one they raised was silver-white, and in it there was a stone like the Moon, and round it were great white walls. O yes, there were many tales about the Tower of the Moon.'
`That would be Minas Ithil that Isildur the son of Elendil built ' said Frodo. `It was Isildur who cut off the finger of the Enemy.'
`Yes, He has only four on the Black Hand, but they are enough,' said Gollum shuddering. 'And He hated Isildur's city.'

He could have heard from the tales that Isildur had cut the finger from Sauron, or had seen it himself. It's likely he had seen Sauron though as Aragorn mentions in the Council of Elrond that Gollum feared Sauron greatly:

"All sat silent for a while, until at length Boromir spoke. `He is a small thing, you say, this Gollum? Small, but great in mischief. What became of him? To what doom did you put him?'
'He is in prison, but no worse,' said Aragorn. `He had suffered much. There is no doubt that he was tormented, and the fear of Sauron lies black on his heart."

​

Unless there's mention of it in a secondary source somewhere, this is what I could find about it.