Bush, a Republican himself, is often heard to remark, unable to stifle his trademark smirk: "Sort of makes me look pretty good, doesn't it?, National Journal reported.
"He is shaking his head like everyone else wondering why they can't get their act together," the source added. "He wants the guy to succeed but thinks a lot of his problems are self-inflicted."
Bush left the office with one of the lowest approval ratings for an outgoing president in recent history; a large percentage of the American public viewed the president as not being competent or even conservative.
Unlike his successor, President Barack Obama, a Democrat, Bush has largely declined to frontally criticize the Trump administration or Trump himself. But Bush, who attended Trump's inauguration last year, was overheard by several people at the time calling Trump's swearing-in "some weird shit."
Bush's father, former President George H.W. Bush, has been less reserved in his criticism of the current commander in chief, writing that he didn't like Trump in a book published last year.
"I don't like him," the elder, George H.W. Bush, says in the book. "I don't know much about him, but I know he is a blowhard. And I am not too excited about him being a leader."