But the 24-year-old is reluctant to return to England, despite his girlfriend saying "he never wanted to leave Newcastle".
Santon, who has been capped eight times at senior level for Italy, returned to Serie A in January - ending his four-year stay at Newcastle in which he made 94 appearances in all competitions.
New Hornets boss Quique Sanchez Flores wants Santon, but the left-back has poured cold water on any potential move.
"I want to stay at Inter," the defender wrote on his official Facebook page.
"I read all your comments and want to say I know nothing about all this.
"Your comments were really very pleasing and I embrace you all with affection. Forza Inter!"