ALBANY — Gov. Cuomo claims he barely knows a fired lobbyist under federal investigation — yet he was close enough to the family to be the secret hand model behind Mario Cuomo’s official portrait, The Post has learned.

The liberal legend Mario had scoffed for years at having his likeness hung among the Empire State’s other leaders, so Andrew went behind his back to have the work secretly created from a 1989 photograph.

But the artist demanded it include Mario’s hands clasped on his knee, even though the photo didn’t clearly show his mitts.

“The artist insisted that he needed to see the Governors [sic] hands to paint them,” Howard Glaser, Andrew’s former director of state operations and Mario’s senior advisor, wrote in a private Facebook post obtained by The Post.

Enter Todd Howe, who is being probed by the feds for lobbying work he did for three firms that are part of the Cuomo administration’s economic-development program, the Buffalo Billion.

He raced down to the painter’s Maryland studio and literally lent a hand.

“The artist painted Todd’s hands into the painting to complete the work. So, yeah, it’s actually Todd Howes hands you see painted in the final portrait!!!!! Classic!” Glaser wrote.

Peter Cutler, a former Cuomo spokesman who is also named in a federal subpoena, replied, “Todd told me, saying it was pretty nerve-wracking — as I’m sure we can all understand,” he wrote.

“Thank God GAMC [Governor Andrew Mark Cuomo] pushed to get the portrait done & installed.”

The artist, Simmie Knox — who also did official portraits for then-President Bill Clinton and First Lady Hillary — recalled Howe giving guidance on how they wanted the painting done, but clammed up when he found out that the lobbyist was under a federal probe.

Gov. Andrew Cuomo presented the painting to his dad as a birthday gift at a 2012 ceremony.

Cuomo spokesman Rich Azzopardi said last night that he could not confirm the Howe story.

“I‘ve asked around. No one here has ever heard of Todd Howe’s involvement with the governor’s portrait,” he said.

Cuomo on Tuesday denied being close with the lobbyist.

“I wouldn’t call us close friends,” he said. “He worked for the state for a number of years, but I had no knowledge of his personal situation.”