Speaking at an event in Los Angeles this week, Clooney, 57, claimed that history was repeating itself in the case of Meghan and Diana, warning: "we've seen how that ends".
The "Money Monster" star laughed off suggestions he could be a godfather to Meghan and Harry's baby.
Clooney also referenced the leaked letter Meghan sent her estranged father Thomas in August of past year, which Thomas himself subsequently sent to press.
Fair to say the British press's absolute obsession with covering every speck of dirt Meghan Markle treads on is approaching levels of pure insanity, and the tide against the tabloids is slowly starting to turn.
In a 2017 BBC documentary, William described paparazzi who followed her as "a pack of dogs" that "followed her, chased her, harassed her, called her names, spat at her, trying to get a reaction, to get that photograph of her lashing out". You watched me silently suffer at the hand of her vicious lies.
Thomas Markle Snr says the letter was sent by his daughter.
The letter's existence was revealed when five of Meghan's pals anonymously spoke out to defend pregnant Meghan, 37, saying she had tried reaching out to her dad but instead been met with a request to do a photo shoot together.
In the letter to her father, Meghan begged him to stop "victimising her".
"I do want to say, they're just chasing Meghan Markle everywhere", Clooney told World Health Organization magazine during an interview in Los Angeles.
They were also the first people to reveal the existence of the letter and said Meghan wrote it in an attempt to mend their rift privately.
She goes on to complain that Mr Markle has made no attempt to contact her - and chastises him for falsely telling journalists he is the one who has been shunned - a criticism her father refutes.
Meghan has also faced intense interest from the unsparing United Kingdom press since her engagement to Prince Harry was announced in 2017.