Eriksen is out of contract in the summer and is keen to move to the Italian club.
Personal terms are not expected to be a problem for the 27-year-old but the two clubs are currently apart in their valuation of the player.
Inter Milan have offered £8.5m for Eriksen but Tottenham value the Denmark international at double that fee.
Eriksen played 90 minutes in the 2-1 victory over Middlesbrough on Tuesday but his name was jeered by fans before the match.
Tottenham head coach Jose Mourinho praised the midfielder for his professionalism and believes he can hold his head high if he does leave the club in January.
"He played very well, very professional which is what I expect from him," said Mourinho.
"If his decision is to leave, I think he has to leave with his head up, if he gives everything which is what he tries to do for the team."
When asked if there was any news on Benfica's Gedson Fernandes, who has completed his medical ahead of his move to Tottenham, Mourinho added: "Nothing."
Argentine pair Erik Lamela and Giovani Lo Celso both scored in the FA Cup third-round replay win, setting up a fourth-round tie at Southampton, and Mourinho says both are progressing superbly.
"I am happy with Lamela and Gio. Lamela was out for so long, he has been coming back step by step," he said.
"Playing 20 minutes here, half an hour against Liverpool and 90 here. You could see his fitness is coming.
"And Gio again has been step by step. He was so so good against Liverpool and so so good here again. I am happy with the boys. They played with intensity. And I am happy with result obviously."
Sky Sports will bring you the very latest news from the January transfer market with the return of three shows.
Start your day with Good Morning Transfers at 9am as our team of reporters bring you the latest news and insight. Transfer Talk then follows at midday delivering analysis of the biggest stories. Then join us at 7pm for the definitive round-up of the day's news with The Transfer Show.
Meanwhile, the Transfer Talk podcast will also be back at the turn of the year with more expert analysis from here and across the continent.
And as well as tuning into Sky Sports News, don't miss a thing with our dedicated Transfer Centre blog.