Citing unnamed intelligence officials, Britain's Sky TV reported on Monday that IS "terrorists" have advanced plans to "murder Jewish children in Turkey, targeting kindergartens, schools and youth centres".
The report came on the same day that Israel advised its citizens to leave Turkey "as soon as possible," warning of the risk of jihadist attacks.
In a phone conversation with the president of the Turkey's Jewish community, Ishak Ibrahimzadeh, Rivlin said he was concerned over reports of threats to the community.
"We are very worried about the information we are receiving, and following the situation closely with the relevant authorities in Israel and Turkey," Rivlin said in a statement.
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The offices of Israeli Prime Minister Benjamin Netanyahu and Turkey's foreign ministry have declined to comment on the Sky report.
Three Israelis were among four people killed in a March 19 suicide bombing in Istanbul.
An Iranian was also killed and 39 people wounded when a man blew himself up on a shopping street in the heart of the city.
The Turkish government said the bomber had links to IS.
The group has been blamed for four bombings that have rocked Turkey in the past eight months, including a massacre at a peace rally in the capital Ankara in October that claimed 103 lives.
Sky reported on its website that unidentified "intelligence officials" said that a fresh attack was imminent, based on information from six IS operatives arrested in southern Turkey.