The 23-year-old spent this season on loan at Olympique Marseille and could reunite with Marcelo Bielsa at the Stadio Olimpico.
“He is a player who can and must improve, with marvellous technique, a right-sided forward who loves to cut back in,” agent Fabrizio Ferrari told Radiosei.
“He left Bielsa on very good terms. Lazio? At this moment there is nothing, no direct contact and no negotiations.
“There could well be interest for him, as there has been for others trained by Bielsa. I do have a rapport with (Lazio director Igli) Tare, but we never talked about Thauvin.
“He did not enjoy Newcastle and would be better off in Italy, France or Spain. He’s a valuable player, worth a lot more than €5m.
“When a big club like Lazio arrives, it is only normal he is flattered by their interest, but for now there are no negotiations.”