England international Welbeck sat out the Gunners’ Premier League match against Hull City away from home at the KC Stadium on Monday.
The former Manchester United striker missed the game due to a knee problem, which has kept him out of training so far this week.
Arsenal will take on Swansea City at the Emirates Stadium on Monday, and ahead of the match, Wenger has revealed that Welbeck is not fit at the moment.
“Welbeck is doing better but he is still not in training, he has missed now more than a week,” the Frenchman told Arsenal’s official website. “There is no major damage but we have to see how it progresses over the next two or three days.”
Welbeck joined Arsenal from United in the summer of 2014 and has been an important player for the Gunners.
The 24-year-old has scored four goals and created 29 chances in 25 Premier League appearances, while having a pass accuracy of 82% and a shot accuracy of 53%.
Another Arsenal player who is not training at the moment is Wales international midfielder Aaron Ramsey, but Wenger is hopeful about his situation.
“From the Hull match we had Ramsey who took a big kick, he is getting slowly better,” said Wenger. “He could be back in training soon.”
Arsenal will head into this weekend’s round of matches in the Premier League placed third in the table with 70 points from 34 matches.