LA Galaxy striker Keane, 32, missed Friday's 6-1 loss against Germany with an Achilles injury, but has since returned to training ahead of the midweek match in Torshavn.
However, Trapattoni, whose side are third in Group C after two games, will be without Andy Keogh after he suffered a concussion following a collision in training on Saturday.
A spokesman for the Football Association of Ireland (FAI) said: "Following training this morning in Gannon Park, Robbie Keane has been ruled fit to travel with the squad for Tuesday's match against the Faroe Islands.
"Andy Keogh suffered a knock to the head in training on Saturday. He was observed overnight by the FAI medical team and has been ruled unfit to travel to the Faroe Islands this afternoon due to mild concussion."
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