Jones has fast-tracked 19-year-old Arundell into his pre-Australian tour training squad.
And England's Australian coach revealed that, in the London Irish fullback, he instantly saw some of the same qualities that prompted him to give 20-year-old Giteau a Test debut when he was in charge of the Wallabies back in 2002.
"The reason I have compared Arundell with Giteau is a similar story," Jones told reporters on Tuesday.
"You get reports through on young players, and where there is smoke, there is usually some fire.
"I remember getting a sevens report on Giteau, what he could do, and then you go and watch him play. Within five minutes you can generally work out whether he's got it or not, whether he's got something special."
Jones saw that "something special" in Arundell when he watched him play for Irish against Wasps earlier this month, reckoning he was impressed with the way he responded to making an early handling mistake for a knock-on by then scoring a superb individual try.
"Giteau was the same," added Jones. "I went to watch him play halfback for his club, and within five minutes you could tell he had something about him.
"But then the hard part comes mate, when they've got to work really hard, they've got to not believe what's being said about them, that they're not kid wonder, that they've got to apply themselves to the task - and that's when the real player comes through."
That's what Giteau did, going on to make 103 appearances for the Wallabies over a 14-year period.
Arundell's first selection in the camp has opened up the possibility of him being a bolter for the three-Test tour in July after scoring 11 tries in 15 matches for Irish and England U20s this season.
"Obviously, there's been a fair bit of publicity about the young boy, but we'll just wait and see," said Jones.
