In the Half-Blood Prince, Dumbledore explains his theories to Harry. He shows him memories about Voldemort's youth, his interest in Horcruxes, his interest toward Hogwarts's founders and how he got some of their old items.
He also explains that Voldemort would probably have seeked then something belonging to Ravenclaw and something to Gryffindor.
"The remaining two, assuming again that he created a total of six, are more of a problem, but I will hazard a guess that, having secured objects from Hufflepuff and Slytherin, he set out to track down objects owned by Gryffindor or Ravenclaw. Four objects from the four founders would, I am sure, have exerted a powerful pull over Voldemort's imagination. I cannot answer for whether he ever managed to find anything of Ravenclaw's. I am confident, however, that the only known relic of Gryffindor remains safe."
Dumbledore pointed his blackened fingers to the wall behind him, where a ruby-encrusted sword reposed within a glass case.
(Half Blood Prince, Chapter 23, Horcruxes) - emphasis mine
He's obviously telling Harry that the only know relic of Gryffindor is his sword, and that it's safe in his office.
But we do know about another item that belonged to Gryffindor himself: The Sorting hat told once in his (its?) song that he used to be Gryffindor's.
While still alive they did divide
Their favorites from the throng,
Yet how to pick the worthy ones
When they were dead and gone?
Twas Gryffindor who found the way,
He whipped me off his head
The founders put some brains in me
So I could choose instead!
(Goblet of Fire, Chapter 12, The Triwizard tournament) - emphasis mine
Surely Dumbledore was perfectly aware of this: he was present when the hat sang this, and I'm sure he even knew it before (he had lived in Hogwarts for... almost ever, and more specifically, had shared a room (his office) with the Hat for decades.
Did he forget? (Dumbledore??) Did he purposely omit to count the Hat? (but then why?)
(Of course, this would not have changed a lot of things, the Hat was just as safe as the sword, in the same office, but he could have said "I'm confident the only two known relics of Gryffindor remain safe" then pointed at each one of them, and I don't understand why he didn't...)