The Blackstone Group’s tenure as a guest at Hilton Hotels is not coming to an end, by any means. But the investment manager, which took Hilton private in 2007 for $27 billion, is showing early signs that an eventual exit strategy is on its mind.

According to documents filed with the U.S. Securities and Exchange Commission, Blackstone is preparing to sell a $1.25 billion stake in Hilton, or about 4 percent of the company, based on an estimated total value of $30 billion when earnings multiples and comparable values of rival hotel giants such as Starwood and Marriott are taken into account.

Blackstone is telling would-be investors the money will be used to help pay down Hilton’s $15 billion debt load. But a successful offering would also help establish a hefty value for the hospitality company, which