The pair are in line to join Chris Evans on the cast of Bong Joon-ho's movie, reports Variety.
Evans is said to be in final negotiations for a starring role in the film, which has been written by The Host screenwriter Joon-ho.
Snow Piercer is believed to centre on a group of people travelling across a frozen world on a train.
Oldboy helmer Park Chan-wook is attached to produce the film.
Bell most recently leant his voice to The Adventures of Tintin.
On Tuesday (January 17), Swinton received a BAFTA nomination for her role in We Need to Talk About Kevin.
Watch the We Need to Talk About Kevin trailer below: