Coquelin sustains broken nose against Everton
Coquelin was seen with blood pouring from his nose following a clash of heads with team-mate Olivier Giroud - who scored the opening goal of Sunday's game in the 39th minute - on the hour mark.
The midfielder returned to the field but was forced off just prior to Tomas Rosicky's late second after being struck in the face by the ball, causing his nose to bleed further.
Asked if Coquelin had broken his nose, Wenger replied: "Yes. I don't know whether he will need surgery or not."
Questioned on his decision to keep Coquelin on the pitch after his collision with Giroud, Wenger added: "They [Arsenal's medical staff] told me he was bleeding but that he could stay on.
"The second time he was hit again so after that I had to take him off. I had been told by the medical people that he could stay on.
"He wanted to stay on. He didn't play here for a long time so now that he plays, of course he doesn't want to come off the pitch."