The founding president of WADA, Dick Pound, told Britain's Sunday Times newspaper that such a ban was "not impossible".
Friday saw the International Association of Athletics Federations (IAAF) uphold an international ban on Russia's track and field competitors first imposed in November after a WADA team led by veteran Canadian sports administrator Pound revealed state-sponsored doping and mass corruption in Russian athletics.
The Russia team is now ruled out of all events in athletics in Rio, although Russian athletes training outside the country can apply to compete as neutrals at the August 5-21 event in Brazil.
But there are fears that the scale of Russia's breaking of doping rules extend beyond just track and field, with swimming said to be another sport that has broken doping rules.
In May, WADA set up a new investigation under Professor Richard McLaren, a Canadian law professor and longstanding member of the Court of Arbitration for Sport (CAS), into allegations of state-backed doping at the 2014 Sochi Winter Olympics in Russia.
Grigory Rodchenkov, the former head of the Russian lab now living in Los Angeles, also gave an interview to the New York Times last month in which he said he switched tainted urine samples for clean ones at the doping lab used for the Sochi Games, with help from people he believed to be officers of the Russian security services.
"If his report indicates transgressions of any kind, then there will be a precedent-setting opportunity to demonstrate our collective commitment to cleaning up sport," added the veteran British sports administrator, who reiterated WADA's support for the IAAF ban on Russia.
"The world will be watching."
Reedie, asked by AFP if he agreed with Pound that a blanket ban on Russia was possible, replied: "I think Dick called that the 'nuclear option'.
Reedie, pressed on what he meant by "precedent-setting action", added: "WADA does not have the power to determine which sports do what.
"If McLaren produces detailed corroborative evidence that goes beyond athletics, we are concerned... We will respond firmly and effectively."
Meanwhile Reedie repeated his calls for increased WADA funding from national governments and also suggested that, for the first time, broadcasters and media rights-holders might want to contribute to the budget.
Reedie added that 0.5 percent of the worldwide sports television rights market would produce a WADA budget of $175 million and that it was in the rights-holders' interest to promote clean sport.
Russian President Vladmir Putin has labelled the IAAF's ban on his country's athletes as "unjust and unfair".
But IAAF president Sebastian Coe, who won Olympic 1500 metres gold and 800m silver for Great Britain at the 1980 Moscow Games, wrote in Britain's Sunday Telegraph: "We have not prevented clean athletes from Russia from competing, rather the Russian system has cataclysmically failed their clean athletes.
