ChronicleLive says Newcastle, Tottenham and Manchester United are all watching the Italy international, 20.
Scalvini is on a deal with Atalanta to 2028.
Newcastle see Scalvini as an alternative to Crystal Palace defender Marc Guehi, who they tried for over the summer.
Toon manager Eddie Howe said last week: "It's unpredictable at the moment. It's very difficult to see what is going to happen. I know no one wants to hear it, but January is always a difficult window in every window so I don't think we should necessarily go into it expecting any different to any other previous January.
"Transfer trading, generally, was down last summer compared to the previous summer so will this January follow suit and it's quieter across the board? Possibly, yes. These are things that don't go in favour of a busy window so without wanting to make predictions, I'd be surprised if it deviated from that."