Arsenal maintained their push for the Premier League title on Saturday with a 4-1 victory over struggling Sunderland at the Emirates Stadium.
However, full-back Monreal had to be replaced by Carl Jenkinson at half-time due to a foot complaint and Koscielny, the scorer of Arsenal's fourth goal, also failed to complete the match after being hampered by a back problem.
Wenger allayed fears over the fitness of the duo, revealing the pair remain in contention for Arsenal's trip to the Britannia Stadium.
"Laurent Koscielny has a back problem," he said. "Nacho Monreal has a foot problem. I think both of them should be fit for next week."
Record signing Mesut Ozil (thigh) missed the encounter with Gus Poyet's charges, while fellow midfielder Jack Wilshere played 90 minutes despite struggling with a hamstring complaint.
Wenger believes neither injury is serious.
"Mesut Ozil has a thigh problem but should also be available next week; he is in the dressing room now," the Arsenal boss added.
"Jack Wilshere has a tight hamstring, I don't know if it is bad or not. They (the physios) told me it's not too bad."
