Russell was excluded for the opener against Ireland, which ended in a 19-12 defeat at Aviva Stadium, with 23-year-old Adam Hastings filling the No 10 jersey.
The Racing 92 star left the team hotel on Sunday 19 January after an alleged drinking session and didn't turn up for training the next day.
After Saturday's defeat Scotland head coach Gregor Townsend was asked about the potential of the 27-year-old, who has 49 caps, coming back into the fold for the England match.
"We will see. It is not something I have thought about since the end of the game," said Townsend.
"We had two weeks training and cohesion was very important in our selection this week. Players who missed two or three days training did not get selected for that. I believe cohesion helped how we played today. When you have five or six training sessions before you play Ireland away you have to make sure your players are in those... For anybody who has missed the last two weeks it will be difficult to get into a squad."
It is understood that Russell was not at the squad's training base - the Oriam centre at Edinburgh's Heriot-Watt University campus - today as training resumed following the return from Ireland.
It means Hastings is primed to resume in the playmaker role in Saturday's big game, with questions over when Russell is expected to be back and his involvement in the rest of this Six Nations campaign waiting to be answered.