Sanchez suffered a dislocated ankle and tendon damage while playing for Chile against Colombia in October.
The need to have an operation meant three months on the sidelines, curtailing the early stages of his loan stay at San Siro from Manchester United.
Inter's head of medical services Piero Volpi told La Cuarta he is optimistic about Sanchez's speed of recovery, with the 30 year-old aiming to resume work with a ball in the near future.
"It is a delicate injury, but the recovery is going very well, the deadlines are being met," he said. "Mid-January [is the return date] but we'll see. Alexis could even come back a little earlier if all goes well.
"He has not yet done work with the ball, but we hope that in the next few days we will have news about it. Everything is going well."
Sanchez scored on his only Serie A start for Inter, a 3-1 win at Sampdoria where he was later sent off, and has made four appearances overall for Antonio Conte's side.
Inter's first game of 2020 is away to Napoli in the league on January 5, while they host Atalanta a week later.