The Germany international sustained an ankle injury in Saturday's 2-1 FA Cup semi-final win over Reading.
Wenger revealed that the former Werder Bremen man has not trained all week, giving Arsenal a concern at the back as they seek to narrow the gap to Chelsea to seven points.
"Mertesacker is still in the treatment room," Wenger said. "I don't know if he's available. He is 50-50 at the moment. He has not practised at all."
Alex Oxlade-Chamberlain is still on the sidelines because of a groin problem and Mikel Arteta is likely to be short of fitness despite returning to training.
Arsenal welcome Chelsea to the Emirates Stadium with Wenger hoping for a for first win over managerial foe Jose Mourinho, who he has not beaten in 12 attempts.
The hosts approach the game on the back of nine straight wins and with just three defeats to their name in 2015.
"We have passed many tests recently. We have another test on Sunday against Chelsea that we want to pass," Wenger added.
"We have an opportunity to show our improvement is consistent. Our first target is to continue to win and strengthen our position.
"We have been close to beating them a few times. The result on Sunday will just be down to the performance on the day."
