During the battle between Naruto and Sasuke in the original series, Naruto got one tails cloak from Kurama. That means he could use Kurama's red chakra. When Naruto uses his regular chakra of blue colour, his rasengan looks blue. But it didn't turn red when he had one tails cloak. Why?
While reviewing the fight scene, I'd like to point out something that I noticed.
Towards the beginning of Naruto and Sasuke's battle, Naruto's Rasengan was its normal blue color, as shown here. This occurrence was prior to Naruto gaining the 9 Tails Cloak.
Towards the end of the battle, while Naruto's Rasengan was forming, I noticed that this ones color was actually more of a purple color than the normal blue (albeit not red either). This is shown here
Purple is a combination of the colors Blue and Red. So with that information, we can deduce that the chakra used to perform Naruto's final Rasengan was a mixture of Naruto's blue chakra and Kurama's red chakra.