The Netherlands international left PSV Eindhoven in the summer of 2021 to join the Nerazzurri, who turned to the 26-year-old to replace Achraf Hakimi.
Dumfries immediately cemented himself as Simone Inzaghi's first choice on the right-hand side and enjoyed a strong first campaign with five goals and seven assists in 45 matches.
The former PSV man has continued to provide an attacking threat on the right for Inter in the 2022-23 season, coming up with two goals and three assists in 20 games in all tournaments.
Dumfries has also started all four of the Netherlands' World Cup 2022 matches so far and produced a man of the match performance in his side's last-16 win over the USA on Friday.
The Inter defender set up Memphis Depay and Daley Blind to put the Netherlands 2-0 up before the break, and he volleyed home unmarked at the back post late on in that 3-1 victory for his side.
Chelsea have been strongly linked with a move for Dumfries in January, while Tottenham Hotspur have also been credited with an interest in the Dutchman.
However, the London rivals have now been joined in the race by Real Madrid, according to Fichajes, who claim that Carlo Ancelotti views Dumfries as an ideal option to succeed Dani Carvajal.
The report adds that Carlo Ancelotti has been left impressed with Dumfries's attacking qualities, and the defender would jump at the chance to sign for the Champions League holders.
Inter have Dumfries under contract until 2025, and the Serie A giants are reportedly demanding between €50m (£42.9m) and €60m (£51.4m) to sanction a sale in 2023.
Furthermore, Inzaghi's side are already believed to be looking at potential replacements for Dumfries, and the Nerazzurri have earmarked Angelo Preciado and Juan Cuadrado as possible successors.
Following the Netherlands' last-16 win over the USA, Dumfries was questioned by the press on links with Chelsea, who are supposedly willing to exceed Inter's asking price to beat Real Madrid to his signing.
However, the right-back remained tight-lipped on his future, telling reporters: "Of course it's a big compliment to be linked with Chelsea, but playing for Inter it's a big compliment too. Chelsea move in January? I'm focused on nothing else but national team and Inter."
Dumfries has totalled seven goals and 10 assists in 65 matches for Inter across all competitions, and he has already won the Coppa Italia and Supercoppa Italiana at San Siro.
The 26-year-old is expected to keep his place in the Netherlands side when they face Argentina in their World Cup quarter-final on Friday.