Calcalist quoted TI spokeswoman Whitney Jodry as saying that the company refrains from commenting on rumors.
If negotiations lead to an agreement, Amazon would become a rival to Apple and Samsung, which also designs their own chips.
TI is currently offering chips for Amazon's Kindle Fire HD device. However, TI is also offering processors for Barnes & Noble's Nook devices.
Earlier this month Texas Instruments announced that it wanted to sell its mobile processors division as the smartphone market had become less attractive for the company to invest.