The 21-year-olds agreed to terminate their contracts early, according to the Yorkshire Evening Post.
They were expected to be let go at the end of the season when their deals were due to expire.
The McKays have now joined Championship rivals Cardiff City on trial.
Leeds snapped up the siblings – the sons of football agent Willie McKay – from Doncaster Rovers in January 2016.
They were brought to Elland Road in a bid to boost the Under-23 squad.
Paul, a central defender, made just one senior appearance for Leeds in last season’s FA Cup defeat at Sutton United.
Striker Jack never featured at first-team level and spent last season on loan with Scottish League One side Airdrieonians.
Cardiff are looking to bolster their reserve team and the McKays featured in yesterday’s 3-3 draw against Charlton Athletic.