The meeting comes less than two weeks after the Christchurch mosques massacre, in which 50 people were killed.
A video of the terror attack, in which a lone gunman opened fire at two mosques during Friday prayers, was live-streamed on social media.
Mr Morrison will tell the executives his government is drafting laws that would make it illegal for the platforms to not remove such footage as soon as possible, according to The Courier-Mail.
The legislation also would allow the government to declare footage of an incident filmed by a perpetrator being hosted on such sites as "abhorrent violent material", creating a separate criminal offence.
The longer any videos were left up after being reported, the greater the penalties social media platforms would face.
Facebook took down 1.5 million posts of the footage of the Christchurch shootings. It has said none of the 200 people who watched the live video of the massacre immediately reported it.
"The first user report on the original video came in 29 minutes after the video started, and 12 minutes after the live broadcast ended," Facebook vice president Chris Sonderby said in a statement last week.
The online giants are also being urged to ensure they protect the personal information of Australians who use their platforms.
The federal government plans to force them to cough up more cash if they breach Australian privacy laws.
Under proposed changes to the Privacy Act, online platforms that seriously or repeatedly breach privacy laws would be fined $10 million, up for the current penalty of $2.1 million.
Alternatively, they could be charged three times the value of any benefit obtained by misusing information or 10 per cent of their annual domestic turnover, depending on which figure was greater.