Inter beat off competition from Everton to sign the 26-year-old Dutchman from PSV Eindhoven last summer and splashed an initial €12.5m to land him.
Dumfries has been a regular for Inter this season, but the Italian giants are prepared to sell him this summer if they make a healthy profit.
Tottenham are looking at a possible deal for Dumfries and are ready to put in a bid of around €23m.
However, it is suggested that Inter want €40m before they agree to allow the Netherlands international to depart the San Siro.
Tottenham look likely to have to substantially improve on the €23m they are hoping to pay if they are to be able to land Dumfries.
Boss Antonio Conte wants to add a right-sided wing-back to his squad and Dumfries could be seen as the answer by the Italian tactician.
Spurs signed Emerson Royal from Barcelona last summer, but he is expected to be allowed to leave for the right price.
