Real estate investment firm Starwood Capital Group chief executive Barry Sternlicht has made an offer for Saks Inc, the New York Post reported on Friday, driving the luxury department store chain's shares up 8 percent.

Sternlicht's offer is in addition to a bid by Canadian retailer Hudson's Bay Co and a possible offer by a Middle Eastern sovereign wealth fund, most likely Qatar, the newspaper reported on its website, citing sources.

The New York Post reported Sternlicht has offered between $17 to $18 per share, roughly equal to Hudson's Bay offer, but that initial bids may have been for $15 to $16 per share. Saks shares ended trading at $15.89 on Friday, giving it a market value of $2.2 billion.

Sternlicht, unlike Hudson's Bay, envisions Saks CEO Steve Sadove remaining in his role and would allow him to collect a change-of-control payout worth upwards of $20 million, the newspaper said.

Starwood declined to comment while representatives of Saks, Hudson's Bay and Qatar's sovereign wealth fund did not immediately respond to requests for comment.

New York-based Saks has appointed Goldman Sachs Group Inc to explore a sale, the New York Post reported on May 21.