Ford, who has played 91 Tests for England since 2014, limped off the field six minutes into his Sale side's game with Saracens while suffering a torn thigh muscle on the weekend.
Ford and Mitchell were paired in four of England's five Six Nations games last season. However, Ford missed the New Zealand tour due to an Achilles injury.
Marcus Smith played first five-eighths in both Tests in New Zealand which the All Blacks won 16-15 (Dunedin) and 24-17 (Auckland).
Sale's director of rugby, Alex Sanderson, said they didn't have a definitive verdict on Ford's injury.
"The initial report from the scan is that it's a tear, so it was the right decision to bring him off at the time.
"We haven't got anything definite to tell you. We don't know the length of time that it will take to rehab at this point."
Mitchell, who has played 15 Tests, has yet to appear for his Northampton club this season. He has a neck injury. He started training with the club team with the injury but then had scans and treatment.
The Northampton club's director of rugby, Phil Dowson, said there was no timeline for when Mitchell could be available.
"It's up in the air. It's hard to make a short or long-term plan when you don't have that information. He is feeling a bit better on the back of some time off. He's probably bored more than anything else, but he's also frustrated because there is no timeline towards it.
"What you don't want to do is mess around with it. We're trying to be quite conservative with it, give it time. The less invasive in those sorts of things the better."
Another Sale player who could be in doubt is 53-Test flanker Tom Curry. He suffered a head injury in the opening club game of the season.
Sanderson said they were taking no chances with his recovery.
"It's just very structured, the return to play, and they have to feel 100 per cent fine with the increased intensity tests they have to go through.
"If they don't feel fine, then it is all delayed. It's not a setback, you just stop the process there, then revisit it the day after."
Curry had tried to come back but did not feel right.
"I just said, Tom, what is the alternative here? You get concussed again and you're out for months, or you get concussed again and you die. Just look after yourself, take a breath."