Thauvin was loaned back to Olympique Marseille, his former club, in January after failing to break into the starting XI.
The 23-year-old, signed for a reported £13million last summer, has also struggled at the Stade Velodrome.
And he is due back on Tyneside in July for the start of pre-season training.
However, Newcastle, likely to be playing in the Championship next season, are ready to cut their losses with Thauvin, who signed a lucrative five-year contract last summer.
According to the Corriere dello Sport, Inter could attempt to sign Thauvin on loan with a view to a permanent move after making contact with his agent.