The 23-year-old had two plates inserted in his face after sustaining the injury in a defeat by Harlequins on December 3.
However, the Premiership club has claimed that Itoje is around "three or four weeks away", rendering him fit for the start of England's Six Nations title defence against Italy on February 4.
The British and Irish Lion could potentially be back for the final two rounds of Saracens' Champions Cup group campaign against Ospreys and Northampton in January.
"Maro is probably three or four weeks away," Saracens director of rugby Mark McCall told reporters. "He went to see the specialist who said a maximum of six weeks and he's already done a week and a half."
Itoje, who has 14 caps, started every match as Eddie Jones's England side won the 2017 title.