Their petition was mentioned by senior counsel Colin Gonsalves before Chief Justice of India Altmas Kabir at the latter's residence for urgent hearing.
The convicts have challenged the rejection of their mercy petition on the ground of inordinate delay in the decision.
Gonsalves wanted an urgent hearing suspecting the convicts were likely to be executed on Sunday.
But the court refused to grant an urgent hearing in the absence of any cogent document showing that executions were imminent.
Veerappan's elder brother Gnanaprakash, Simon, Meesekar Madaiah and Bilavendran were awarded death sentence in 2004 in connection with a landmine blast at Palar in Karnataka in 1993 in which 22 police personnel were killed.
Their mercy petition was rejected by President Pranab Mukherjee on February 13.