Coach Randy Carlyle says Kessel and Bozak are dealing with lower-body injuries.
Clarkson, who took part in the morning skate wearing a full cage, has been out since suffering a broken cheekbone a week ago in a fight with the Sabres' Cody McCormick.
While those injuries shouldn't affect the Leafs' opening-night roster, Franson's status remains in doubt with a knee problem.
If Franson isn't ready by the time the Leafs host the Canadiens on Wednesday, Stuart Percy or Korbinian Holzer could replace him in the lineup.
Veteran defenceman Stephane Robidas will make his pre-season debut Friday night against Detroit after breaking his right leg in the playoffs.
Robidas could have been ready over a week ago, but Carlyle says the team's medical staff has been "over-cautious."