Ramsey is still recovering from the painful knock he suffered during Arsenal's 3-1 win over Hull on May 4, while Welbeck is nursing a knee injury.
"From the Hull match we had Ramsey who took a big kick, he is getting slowly better," Arsenal manager Arsene Wenger told the club's official website. "He could be back in training soon.
"Welbeck is doing better but he is still not in training. He has missed now more than a week. There is no major damage but we have to see how it progresses over the next two or three days."
Wenger added that defender Mathieu Debuchy and midfielder Alex Oxlade-Chamberlain have both been ruled out of the match with hamstring injuries, while midfielder Mikel Arteta will also be sidelined due to an ankle problem.