The Chile forward suffered a hamstring injury in the draw at Norwich, while midfielder Santi Cazorla finished the game "playing on one leg" after suffering a blow to his knee.
"At the moment on Alexis, Santi and Mikel (Arteta), we don't know how long they will be out for," Gunners boss Wenger told arsenal.com.
Arteta suffered a calf injury against West Brom last month.
Wenger may provide an update at his Friday morning media conference to preview Saturday's Premier League clash with Sunderland
The Gunners are fourth, two points behind leaders Manchester City, entering this weekend's fixtures.
Arsenal have been rocked by injuries all season and Wenger will not want to be without Sanchez or Cazorla for a significant period as the busy festive fixture schedule nears.
Following the draw at Carrow Road, Wenger faced criticism for selecting Sanchez.
"I would have rested him today but he felt perfectly all right before the game and he declared that he had no problem," Wenger said.
Laurent Koscielny (hip) had to be substituted at Norwich, but could feature against the Black Cats.
The France defender and Theo Walcott will face late fitness tests.
England forward Walcott suffered a calf injury at Sheffield Wednesday in October.
Left-back Kieran Gibbs is back in contention after missing the Norwich match with a calf injury.
Wenger added: "We will make a decision on Saturday on Koscielny and Walcott, they could both make the squad
Gibbs is available again for the weekend."
Midfielders Jack Wilshere (broken leg), Francis Coquelin (knee), Tomas Rosicky (knee) and forward Danny Welbeck (knee) are all out.
Source : PA