Steinway had agreed to a $438 million bid from equity firm Kohlberg & Co. in early June, a deal that came to $35 per share.
But that deal included a 45-day go-shop period that allowed Steinway to discuss better offers and one eventually materialized, The New York Times reported.
The new bid is for $38 per share and comes from an "affiliate of an investment firm with over $15 billion under management," Steinway said, stopping short of naming the bidder.
Kohlberg now has until Wednesday to match the better offer, the Times said.
Steinway was begun in 1853 in Manhattan. It makes pianos, horns and other instruments, the Times said.
The company's headquarters is now in Waltham, Mass., near Boston.
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