Hearts forward Steven Naismith is already out of the matches against Albania and Israel on 17 and 20 November after sustaining a knee injury in the Betfred Cup semi-final against Celtic. Now Scotland could lose another striker.
Celtic manager Rodgers said: “It will depend on Leigh, how quickly he responds to treatment and how hard he works to get fit. He’s getting better and his calf injury is coming towards its end.
“He’s not on the playing field yet but he’s working with the medical team and the sports science team to get as it as he possibly can.
“However, if he is fit for that period he certainly won’t be match fit.”
Naismith has been fine form this season, scoring 11 goals for Hearts and usurping Griffiths as Scotland manager Alex McLeish’s first-choice striker.
Rodgers added: “I feel for Steven Naismith, because he’s made a great start to the season and done really well for Scotland.”