What's the motivation behind this question? I only ask because I've never heard anything like this; OP, have you heard this as a rumor, or urban legend, or seen something that led you to believe it was the case?

Not criticizing the question at all, just curious because this seems like it's from way out of left field.

The answer is no. There is no evidence that the Sphinx was on an island. It is very near to the Nile floodplain but at a higher elevation so it would never have been submerged. There is an interesting debate over the age of the Sphinx though, based on the amount of erosion by rainfall. If the Sphinx really is older than we currently think it is, it's possible that the floodplain may have been higher at some point in the past which could mean that the Sphinx may have been submerged at some point but there is no evidence for this.

There are extreme fringe theories about the Pyramids and Sphinx being much, much older than we think but there's, again, no evidence to support this and they are basically no better than conspiracy theories. These theories vary and some say that the Giza plateau was completely submerged by the sea at some point. If that were true, as the Sphinx is on the Giza plateau then it may have been on an island at some point in the distant past. Very, very unlikely to be true though. The pyramids and the Sphinx inspire a lot of crackpot theories.