Construction materials manufacturer Carlisle Companies has rebuffed Kingspan's informal approach to combine the companies, Bloomberg News reported over the weekend.
Co Cavan-based Kingspan had proposed a deal in recent months, which Arizona-based Carlisle rejected.
But Carlisle signaled it would be open to at least reviewing a more attractive offer, the report said, citing people familiar with the matter.
Kingspan is not working on a formal takeover bid currently, the report said, adding that it could trigger fresh interest from the Irish company as well as other building materials rivals if Carlisle did explore a sale.
Kingspan did not immediately respond to a Reuters request for comment. Carlisle could not be immediately reached for a comment.
As on Friday, the market capitalisation of Kingspan Group and Carlisle was €13.4 billion ($14.34 billion) and $12.55 billion respectively.
Kingspan shares were lower in Dublin trade today.