The Brazilian forward netted 15 goals in Serie A last season, but couldn’t prevent Livorna from being relegated.
But despite their relegation, Amaranto are demanding at least £8m for their star striker’s services, with Southampton believed to be leading the race for his signature.
But fellow Italian side Torino have also expressed their interest, with the striker thought to be eyeing a move back to Italy’s top-flight.
And Livorno president, Aldo Spinelli, has admitted there is interest in the 28-year-old, but a deal is far from being agreed.
He said: “On the Paulinho front everything is still, nothing moves.
“If Torino want Paulinho, then they have to pay £8m upfront, we do not need players in exchange.”