Gov. David Paterson has some unfinished business with News Corp. CEO Rupert Murdoch.

The governor couldn’t help but take a few digs at the media mogul this morning in spite of their “cordial” conversation yesterday, during which Murdoch apologized for oddly linking the polarized public discourse in New York to Paterson’s disability.

“I think I would be willing to on ‘Jeopardy’ with Mr. Murdoch any time,” Paterson joked with WOR’s John Gambling during an early-morning radio interview covered by DN Capitol Bureau Chief Ken Lovett.

Despite the fact that he is legally blind, Paterson graduated high school in three years, went to Columbia University, finished law school and worked in the Queens DA’s office.

(This whole “overcoming adversity” theme is also the focus of one of Paterson’s two 2010 campaign ads).

The governor insisted he and Murdoch are “fine” because Murdoch called to apologize “like a gentleman.”

But then Paterson took one parting shot, asking Gambling: “By the way, does Mr. Murdoch read Braille?”