The concept of giving drug abusers involved in minor crimes the choice of whether to go to jail or undergo rehabilitation was initiated by Russia's anti-narcotics chief, Viktor Ivanov, RIA Novosti reported Monday.
"The question now is about which crimes should be included into this initiative," Medvedev said.
"I instruct the government and the presidential executive staff to review this proposal in a two-month term and submit the decisions to me," Medvedev said.
Around 30,000 Russians die from heroin abuse annually and the country's HIV rate is increasing, RIA Novosti said.
Yevgeny Bryun, chief alcohol and drug abuse specialist in the Russian Ministry of Health, also proposed requiring compulsory drug tests for people applying for jobs.
"I recently came across an employment ad in the United States, which said there would be drug tests for job applicants," Bryun said.
"Every company there has the right for drugs tests. I believe we should have it as well."