The International Association of Athletics Federations (IAAF), along with several other federations, has banned Russian athletes from international competition until the country meets anti-doping requirements.
"It's not happening at the speed I would have liked to see but it is happening," Niggli told the BBC.
The McLaren report also revealed more than 1,000 Russian athletes competing in summer, winter and paralympic sport were benefited from an institutional conspiracy to conceal positive doping tests.
Russia's sport leaders, as well as President Vladimir Putin, have acknowledged the country's doping system was not working and needed an overhaul but have denied allegations of a state-sponsored doping programme.
"We are working with them to see if things can be put into place and a credible system be reinstated in Russia in the coming months," Niggli added when asked about next year's Winter Olympics in Pyeongchang, South Korea.
"We will see where they are when we get closer to the Games. They still have a number of months to do the right thing. The ball is in their camp, they know what they have to do."
(Reporting by Shravanth Vijayakumar in Bengaluru)
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