The Press Association said that it understood Whitbread had been approached informally over a buyout of the firm.
Despite potential interest from elsewhere Whitbread is continuing plans to spin the chain off on the London Stock Market. It is said that it would take a bid of between £2bn and £3bn to see the board sell Costa to a private equity firm.
In April the firm said it was aiming for a “demerger of Costa” within two years, prompting CEO Alison Brittain to say a separation would create “long-term value” for stakeholders.
The company is currently carrying out an overseas expansion, with the new buyer reported to be interested in continuing the expansion and tightening up costs.
Shares in Whitbread rose by almost 2% following the news.