The investigate reporter, best known for his efforts to expose corruption at FIFA, made the startling call in the wake of last week's revelations of widespread corruption at soccer's world governing body.
The shopping centre tycoon is seen by many as a key figure in resurrecting soccer in Australia since being elected chairman of the FFA in 2003.
But according to Jennings, Australia's failed government-funded $46 million bid for the 2022 World Cup, which was ultimately controversially awarded to Qatar, should force his exit.
"I think Frank Lowy should resign immediately, he's led Australian football into disaster," he told the ABC.
The corruption scandal which has engulfed soccer on a global scale has led to the stunning resignation of FIFA President Sepp Blatter, the arrest of nine officials and five sports media and promotions executives and involves accusations of bribes totalling more than $US150 million ($A192.91 million).
Jennings alleges Australia has not been immune to this side of the beautiful game, pointing to a $US500,000 ($A643,000) payment he alleges was put in the "private bank account" of disgraced former FIFA vice-president Jack Warner, who is among 14 to have been indicted over corruption allegations.
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