But if Harry does attend, it's sure to come with outcry from royal fans since he pulled out of his grandfather Prince Philip's memorial service in London.
Organisers initially considered the pair for presenting the coveted Best Actress award.
But this was quickly canned because actress Kristen Stewart is up for the award for her role as Princess Diana in horror biopic Spencer.
A source told the publication, "Harry and Meghan were first approached two years ago for the ceremony but politely declined.
"Obviously they'd be a huge coup this year, and could use their appearance to make an impassioned speech of their choosing, most likely [about] Ukraine.
"Show producers Will Packer and Shayla Cowan have lined up some amazing A-list names to take to the stage and Harry and Meghan would be the icing on the cake.
"It's still up in the air, but in all likelihood – especially in the wake of recent publicity – Harry won't attend.
"It would be seen as a final kick in the teeth for the royal family if he did – he's too nervous to fly to London without police protection, but happy to stand up in front of a huge live audience at the Dolby Theatre in Hollywood. Not great optics."
The 94th Academy Awards will take place next Sunday local time in Los Angeles, hosted by Amy Schumer, Wanda Sykes and Regina Hall.
Meanwhile, Meghan Markle is launching her own podcast series on Spotify after she and Harry raised concerns about "misinformation" on the platform.
The pair signed a $34 million deal with the streaming service, but have only recorded one show so far.
