Dumfries joined Inter in the summer of 2021 from PSV Eindhoven for a transfer fee in the region of €12m, with the Italians beating Everton to his signature.
The 27-year-old right-back was a centre of interest for several clubs last summer, but Nerazzurri refused to let the player leave.
Dumfries has been a regular this season for Inter, but some of his performances have come in for criticism.
It has been suggested that Dumfries might leave in the summer transfer window and Newcastle are interested in the Dutch international.
The Magpies have now put in an enquiry about Dumfries, according to Italian daily Gazzetta dello Sport, as they look to find out about his situation.
Newcastle are in pole position to land Champions League football next season and Eddie Howe wants to bolster the depth of the squad.
Dumfries has a contract with Inter until June 2025, but the club might let the Dutch right-back go in the summer for the right price.