Swayman made 23 saves on 26 shots in Thursday's 3-2 overtime loss to the Oilers.
Swayman will be between the visiting pipes in Edmonton on Thursday, according to Jim McBride of the Boston Globe.
Swayman will be between the road pipes Tuesday against the Flames, Jim McBride of The Boston Globe reports.
Swayman is expected to start on the road against Vancouver on Saturday.
Swayman turned aside 27 shots in Tuesday's 8-1 loss to Winnipeg.
Swayman will guard the road goal against the Jets on Tuesday, according to Kevin Paul Dupont of The Boston Globe.
Swayman will patrol the home crease versus Philadelphia on Saturday, Steve Conroy of the Boston Herald reports.
Swayman turned aside 20 shots in Wednesday's 4-2 win over Chicago.
Swayman will protect the road goal versus the Blackhawks on Wednesday, Tracey Myers of NHL.com reports.
Swayman will protect the home net versus Montreal on Sunday, according to Andrew Fantucchio of Boston Hockey Now.