The Daily Telegraph says the Scotland right-back has been in great form for both club and country this season and Tottenham's director of football, Damien Comolli, was at Ibrox to watch the player himself during Rangers' 2-1 win over Hearts at the weekend.
Hutton is a player who would fit in to Ramos' preferred system of full-backs who get forward to provide width in attacks as well as being solid defensively.
An offer in the region of £7 million from Tottenham could test the Scottish club's resolve, however, and a bid is likely to be tabled as soon as the January transfer window opens.
The weekend's match was the third time that Tottenham have had Hutton watched after his performances for Scotland in their narrow European Championship qualification failure alerted the club to his talent.
Comolli left Ibrox after the Hearts match "very impressed" by what he had seen.