The 22-year-old player is valued at £65 million, and the English club wants to keep him as a long-term asset.
According to sources, Pep Guardiola's team is interested in signing Livramento to replace Kyle Walker, who left the club recently.
Newcastle is determined to retain one of its promising young players and is willing to offer a substantial six-year contract extension to keep him at the club.
The proposed deal would tie Livramento to Newcastle until 2028, ensuring the club's investment in him is protected.