The defenders have been sidelined with ankle problems, leaving the Perth side with just four senior defenders fit to play.
Clancy, the former Motherwell and Hibernian defender, has been invited to train with the club this week and has been joined by his fellow Irishman Spillane. The 24-year-old left Cambridge United this month having previously played for Norwich City and Brentford.
"We can't go with four defenders for the rest of the season," said Tommy Wright, the St Johnstone manager. "It would be remiss of me if I didn't bring somebody in going into such a crucial part of the season. We are looking at one or two options."