Mustafi, who has excelled at centre-half alongside Laurent Koscielny since his arrival from Valencia last summer, suffered a hamstring injury in the 3-1 win over Stoke City in December.
The Germany international has missed three games for the Gunners since picking up that knock, a period coinciding with Arsenal's worst run of form this season.
Oxlade-Chamberlain meanwhile has not featured since limping off just 13 minutes after coming off the bench against Manchester City, having suffered a hamstring injury in the second-half of the 2-1 defeat.
While Mustafi and Oxlade-Chamberlain are nearing full fitness, the Gunners will still be without Theo Walcott who is sidelined with a calf injury while Kieran Gibbs is also unavailable due to a knee problem.
"Alex [Oxlade-Chamberlain] looks like he could join in normal training on Saturday," Arsene Wenger told the club's official website.
"From the last game, I think we lose Kieran Gibbs. It's not big damage to his knee but he has inflammation and I don't think he will be available. Danny Welbeck is doing well in training, so we have plenty of options. Theo Walcott will still be short. Shkodran is back in normal training and he will be back in the squad."
While Welbeck is back in full training, Wenger is opting for a cautious approach in reintroducing the former Manchester United striker back into the first team.
Welbeck had been sidelined since May, when he underwent surgery to correct significant cartilage damage in his right knee, a blow which came just 12 weeks after his return from another long-term knee problem.