"Bill Clinton is all of us," Grabien founder Tom Elliott wrote on Twitter along with a clip of Clinton with his eyes closed.
"Chileee, they caught Bill Clinton taking a lil’ cat nap at the Inauguration," gossip site The Shade Room posted on its official Twitter account.
Clinton and his wife, 2016 Democratic presidential nominee Hillary Clinton, attended Biden's inauguration and sat behind former Vice President Mike Pence and former second lady Karen Pence.
Clinton, 74, was roasted online for closing his eyes while Biden spoke.
Former President George W. Bush also attended Biden's inauguration with former first lady Laura Bush. Former President Donald Trump was the first president in more than a century and a half to not attend his successor's inauguration.
Fox News' Matt Leach and Paul Steinhauser and FOX Business' Blake Burman and Thomas Barrabi contributed to this report.