Zakir Naik, a radical television preacher, reportedly left India in 2016 and subsequently moved to largely Muslim Malaysia, where he was granted permanent residency.
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According to Indian media reports, New Delhi asked for him to be extradited in January. The two countries have an extradition treaty.
"As long as he is not creating any problem, we will not deport him because he has been given permanent residency status," Mahathir said at a news conference in administrative capital Putrajaya outside Kuala Lumpur, when asked about the reports.
The reports say India had asked for Naik to be sent back for allegedly inciting youth to engage in terror activities via his hate speeches.
Naik, 52, has described the media reports as "totally baseless and false", adding that he has no plans to return to India until he felt "safe from unfair prosecution".
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In 2010 Naik was reportedly barred from entering Britain after the Home Secretary cited "numerous comments" which showed his "unacceptable behaviour".
In a July 2008 TV broadcast Naik suggested that Al Qaeda was not responsible for flying hijacked airliners into New York's World Trade Center on September 11, 2001, killing almost 3,000 people.
Neither Indian nor Malay officials have confirmed the extradition request or the existence of any charges again Naik.
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