Tavernier picked up an ankle issue against Brentford before the international break and he missed the FA Cup game against Manchester City at the weekend.
Andoni Iraola confirmed the Englishman would miss the game against Ipswich Town on Wednesday, and likely the game at West Ham at the weekend due to the quick turnaround.
Asked if there was a timeline for his return, Iraola said: “No, it's going to be more how he feels.
“We will work with the clinical team. The problem is now we have three games in six days. So even if he's not going to lose a lot of time, he's losing games.”