David Jennings, 50, of Eltham, south-east London, is currently in Highpoint Prison serving a 2.5 year term for attacking a neighbour.
He made his threat to the prison vicar, and is due to be released on 7 January.
The ex-soldier has threatened to appear without warning at a school with a gun, and Greenwich Council chiefs believe a local school could be the target, because Jennings is believed to have a grudge against the council over the treatment of his children in care and their tuition in the borough.
The council has sought a High Court writ against the father of 10. It seeks to ban Jennings from entering or going within 250 yards of any local school.
A Greenwich spokesman told the South London Press: 'We're taking his threats very seriously. School security is constantly under review but if there are any other measures needed at schools at risk they will be in place before 7 January.'