Several news outlets reported that Giuliani, a Republican, also will announce that he is not running for senator but the source couldn't confirm that.
"I don't know where that's coming from," said the source who spoke on condition of anonymity.
Giuliani spokeswoman Maria Comella did not respond to a phone call.
The endorsement would be a boost for Lazio, a Republican former congressman from western Suffolk and eastern Nassau who has been out of office since an unsuccessful 2000 Senate campaign against Hillary Rodham Clinton.
Lazio announced his candidacy against Gov. David A. Paterson, a Democrat who took over for Eliot Spitzer in 2008 and is seeking a full term in 2010. Both may face primary opponents: Paterson from Attorney General Andrew Cuomo and Lazio from Erie County Executive Chris Collins.
Giuliani chose not to run for governor last month. His reported decision to not try for the Senate leaves Sen. Kirsten Gillibrand, a Democrat appointed this year by Paterson, without a major Republican opponent in 2010.
She was losing to Giuliani in polls.
But Giuliani and Cox do not have good relations; Cox defeated Giuliani's favored chairman candidate in recent party elections.