The 21-year-old became the club's record signing in the summer when they agreed a near £30million deal with Roma.
However, the Argentine international has failed to settle as expected and reports have constantly linked him with a move back to Italy - something his father has now claimed is something he would like.
"Erik is not happy and he wants to go back to Italy," he said to Fox Sports Radio del Plata.
"If he can go back to Roma? I don't know. The only thing that I know is that Tottenham doesn't want to let him go in January."
Recent reports claim that Italian champions Juventus want to take Lamela and could offer experienced striker Mirko Vucinic in part-exchange.