The video tape, which was obtained by the privately-owned Channel 2 television station, shows Omri Sharon sitting with two senior leaders from his father's Likud party, one of whom was offering to use party funds to finance Sharon's election campaign.
"I can issue Likud checks today which no one can trace," said Uri Shani, then Likud director.
"It's properly sorted. I mean, I can get him what you want without anyone knowing anything," he said.
Omri is seen on tape sitting with Shani and Likud's former strategic adviser David Spector and listening without replying.
The conversation, which also covers other issues, appears to directly contradict testimony given by both Omri Sharon and Shani to the state prosecutor who is investigating the alleged corruption.
Top police and judicial officials told Channel 2 the tape would likely spur a series of indictments against senior Likud figures in the near future.
Members of the Sharon family have been questioned several times by Israeli police and the national fraud squad over alleged irregular contributions to the 1999 campaign for the leadership of the Likud party.
Omri, who is a Likud deputy, was questioned by police in October.