Saka, who has made 22 league appearances this season and scored eight goals, injured his right leg during Sunday's 3-1 win over Liverpool where he scored the first goal.
"He's been recovering again this week and he looks okay," Arteta told reporters on Friday.
"Tomorrow we have another training session and we are hoping we are going to have a few back," the Spaniard said, adding that midfielder Thomas Partey (30) was progressing well but did not have a date for returning.
Third-placed Arsenal have won their last three matches, but Arteta is wary of David Moyes' West Ham who beat them 2-0 at the Emirates in December.
"He's a really competitive manager who is really good at getting the edge in a game. He waits for the right moment and tries to punish you. They are a really good side. We will have to be at our best to win the game," Arteta said.
The Arsenal boss added that he did not agree with the criticism of his team for their celebrations after Sunday's 3-1 win over leaders Liverpool which rejuvenated their hopes in the title race as defending champions Manchester City close in.
"Managers and teams celebrate a lot. It's so tough to win in this league. It was a big match for us, you could tell from the stadium the atmosphere, it was a great day," he said.
"I've seen managers at the Emirates on their knees, managers going across the pitch. I love it because it brings so much passion and emotion to the game."
Arsenal are level on 49 points with second-placed Manchester City, who have a game in hand on their rivals, with the pair trailing Liverpool by two points. West Ham are seventh on 36.
