The couple were rejecting social media in both a personal and professional capacity as part of their new "progressive role" in the United States, the Sunday Times said.
A source close to the couple told that they had "no plans" to use social media for their new Archewell Foundation and were "very unlikely" to restart utilising platforms personally.
The Duke and Duchess of Sussex, who moved to California last year after abruptly resigning from British royal duties, have previously had prominent presences online.
They amassed more than 10 million Instagram followers to their Sussex Royal account while they were working royals.
But the couple have also previously complained about their treatment on social media, as well as in the British press.
Meghan described past trolling of her as "almost unsurvivable" while Harry issued an unprecedented statement in 2016 denouncing "the racial undertones of comment pieces" and "the sexism and racism of social media trolls".
Last year they launched a wide-ranging non-profit organisation, Archewell, after giving up their "Sussex Royal" brand as part of the terms of their departure from frontline monarchy duties.
They have started other creative ventures, including signing a deal with Spotify to produce podcasts that tell "uplifting and entertaining stories".
This past October, Meghan did a guest spot on a special World Mental Health Day interview for the podcast Teenager Therapy, where she discussed her own battle with social media bullying.
"I'm told that in 2019 I was the most trolled person in the entire world, male or female," she said. "Now, eight months of that I wasn't even visible. I was on maternity leave or with a baby but was able to just be manufactured and churned out.
It's almost unsurvivable. That's so big you can't even think of what that feels like, because I don't care if you're 15 or you're 25, if people are saying things about you that aren't true, what that does to your mental and emotional health is so damaging."