The Italy goalkeeper underwent surgery on Monday after suffering a fracture in victory at Manchester City.
However, while there is room for Spurs to seek permission to sign a replacement, it's likely they will go with Fraser Forster as their new first-choice, with Brandon Austin and Alfie Whiteman to act as cover.
As per the Premier League handbook under rule V.7.6.2, it states: "The temporary transfer of a goalkeeper which in its absolute discretion the board may allow in circumstances it considers to be exceptional."
Given Tottenham's goalkeeper depth, it's unlikely their situation will be deemed as "exceptional" should they request permission to sign a keeper outside the transfer windows.
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play