The Potters and the Gaunts are both said to have descended from the Peverell brothers. Voldemort came from the Gaunt line and was the heir of Salazar Slytherin. Was Harry also the same, or is it that the Peverell brothers were so back in line of ancestry that the divergence of bloodlines digresses the relation?
He's related somewhere, but Slytherin isn't his ancestor.
There was a debunked rumour on J.K. Rowling's old website which mentions this topic obliquely:
Voldemort is Harry's real father/grandfather/close relative of some description
No, no, no, no, no. You lot have been watching much too much Star Wars. James is DEFINITELY Harry's father. Doesn't everybody Harry meets say “you look just like your father”? And hasn't Dumbledore already told Harry that Voldemort is the last surviving descendent of Salazar Slytherin? Just to clarify – this means that Harry is NOT a descendent of Salazar Slytherin.
It is almost certain that Slytherin and Harry are related somehow (the connection with the Peverell brothers ensures this is the case), but the connection is likely to be incredibly distant and probably too far back in their family trees to be meaningful.
Wouldn't the Peverell brothers predate Slytherin? Their exploits have passed into legends most wizards don't believe. Slytherin seems more hard history. Slytherin, the Gaunts, and Voldemort could be descended from one of the other two brothers, while Harry is descended from the one who got the cloak.