Neves has been on the Reds' radar for some time but will face fresh competition for the highly-rated midfielder from their Premier League rivals Chelsea.
Neves has a contract which runs with Porto until 2019 and the Portuguese club are thought to value the versatile midfielder at around £30m.
Neves already has plenty of European experience under his belt as Porto have reached at least the Champions League group stages in 12 of the past 13 seasons.
Neves has been with Porto since he was eight-year-old but is ready for the next step in his career.
Porto last won the league in the 2012-13 season - when Neves was only part of the youth set-up, having made his first-team debut in 2014.