The Toledo Museum of Art said in a statement on its website that last month it was contacted by a representative of the US Justice Department, southern New York region, regarding items purchased from and gifted by Kapoor.
"The Museum will cooperate fully with that agency's ongoing investigation," it said.
Kapoor is currently in custody of Indian authorities for arranging the theft of statues from significant cultural and religious sites across India.
The museum's communications director Kelly Garrow told the Blade newspaper that the investigation into the Ganesha statue, which is believed to have been bought for USD 245,000.
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The museum said that like many other museums across the country, it had acquired objects from Kapoor in the period from 2001-2010.
The most significant of the eight pieces acquired by the Toledo Museum from Kapoor is the Ganesha figure. After the 2006 Ganesha purchase, Kapoor gifted 56 small terracotta idols. While the purchased Ganesha statue had been on public display, the gifted terracotta items have never been so.
One of the images of a Ganesha figure closely resembles the Ganesha purchased by the Museum in 2006 from Kapoor's gallery Art of the Past. The museum has not been asked to turn over the Ganesha statue.
The museum's director Brian Kennedy had also sent a letter to the Indian Consulate in New York requesting assistance in researching the Ganesha's provenance with Indian officials.
The museum said it has not yet received any response from consulate officials.
"The Museum has not been contacted by Immigration and Customs Enforcement or any other government agency in regards to this object and others the Museum purchased from Art of the Past or was gifted by Kapoor," it added.
The National Gallery of Australia had filed a suit in December against Kapoor in New York state. Kennedy said that such legal action against someone in Kapoor's straits was unlikely to be productive, according to the Blade report.