Saka was forced off with a quad injury during Arsenal's 2-2 draw against Bayern Munich last month and was left out of Thomas Tuchel's squad for upcoming England matches.
"We're talking about obviously weeks, let's say after the international break," Arsenal boss Arteta said ahead of the visit of Hull to the Emirates Stadium on Saturday.
"He's going to start hitting the pitch and start to have more activity and see how he feels, but unfortunately he's going to be out for a while."
Konsa was taken off during a 2-1 win at Slavia Prague on Wednesday but is fit to face Hull.
The former Aston Villa defender was recruited in August, partly to provide cover for Saliba during his prolonged absence with a back injury.
Saliba returned to the squad for the first time this season for the trip to Prague but did not play.
Arteta, whose team are top of the Premier League, said he would not stand in the way if coach Zinedine Zidane calls up Saliba to the France squad.
"They have all the information. Now it's about them, about Zinedine in this case, to give the call," said Arteta. "We will accept whatever it is. It's more between them because William needs minutes as well."
He added: "I know how much he loves to be around the national team. It's a new manager, a really exciting one as well, so whatever he's decided is fine for us."
Despite the absence of Saka, Tuchel's squad includes five Arsenal players - Ben White, Myles Lewis-Skelly, Eberechi Eze, Declan Rice and Konsa.
"It is a proud thing to have a big English core in the national team," said Arteta.
"Our club, it is something that is part of our identity. They are super happy to be back, you can see that. Let's focus on tomorrow and then after that they can go and do their bit with the national team."
English Premier League
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