TMW says Toon boss Rafa Benitez wants to sign the 23-year-old left-back when the transfer window opens next month.
Newcastle are on the hunt for reinforcements ahead of Amanda Staveley's takeover from Mike Ashley, and Palmieri has apparently been marked as a target to strengthen their backline.
“But I am under contract with Roma. I'm flattered by stories such as these. However, I want to stay here in Rome. I am happy here."