The Reds have been linked with the Italian international, with suggestions the club have identified Jorginho as their number one defensive midfield target in the summer.
But the 26-year-old is in demand after shining for the Serie A leaders with performances that will be attracting attention from elsewhere.
Including, according to the Times (and replicated in the Mirror), the two Manchester clubs.
The report suggests Jorginho will be in demand at the end of the season, with Pep Guardiola and Jose Mourinho also keeping track of his situation in Italy.
The Brazilian-born star joined Napoli from Hellas Verona in 2014 and has made 22 league appearances this season.