Ben Barba changed the codes after being released from the NRL in 2016.
Athletes who fail drug tests for marijuana and cocaine can reduce their bans from four years to four weeks.
The World Anti-Doping Agency (WADA) is holding a conference in Poland this week that will be attended by international anti-doping agencies.
During the conference it will be discussed that if athletes caught with these recreational drugs in their system can prove that they were not used to improve their performance, they can significantly reduce the bans.
Implementation of these substances out of competition will take three months, but this can be reduced to just four weeks if the athlete attends a detox and rehabilitation program.
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Under current rules, athletes face a two- to four-year ban on finding cocaine in their system.
If the changes were approved at the conference, the new regulations will be part of Wada's code, introduced in January 2021.
Although under the current code, an athlete may be banned for four years for taking cocaine, in practice it is less than in recent years.
Peruvian football star Paolo Guerrero was given a 14-month suspension in May 2018, though that ban was lifted in time for him to play in the World Cup in Russia.
Ben Barba received a three-month ban from the NRL after testing positive for cocaine after the Sharks' grand final victory in 2016 and was subsequently dismissed.
However, he was free to play elsewhere in the world, and the following year he played rugby for Toulon and a league for St Helens.
The change will be controversial for those for whom anti-doping is a public health mission.
"Our role is anti-doping, so it has to do with sports, and health care is for the countries more than us," WADA Director-General Olivier Niggli told AFP.
David Sharp of the Australian Doping Agency, Asada, told The Daily Telegraph that rehabilitation should be the main focus for athletes caught on recreational drugs.
"When used in a social context, you have the aspect of well-being and rehabilitation as priority verses 'throw it out of the sport, take it away, which gives them network support,'" Sharp told The Daily Telegraph.
"This is for consideration for the type of use, because when used, the welfare aspect should be a priority and be completely removed from the sport.
"Nobody knows that an athlete is out of the sport of error."