By Greg Roumeliotis Oct 17 (Reuters) - Tilman Fertitta, the billionaire owner of the Golden Nugget Casinos, has approached U.S. casino operator Caesars Entertainment Corp about merging it with his own gaming empire, people familiar with the matter said on Wednesday. Fertitta, whose holdings also include the Houston Rockets National Basketball Association team and restaurant and entertainment company Landry's, is contemplating a reverse merger in which Caesars would be the acquirer, and Caesars shareholders, including private equity firms Apollo Global Management LLC and TPG Global, would remain shareholders in the combined company, the sources said. It is unclear whether Caesars will find any offer from Fertitta attractive, given the company has a market capitalization of $6.3 billion and Fertitta's net worth is pegged by Forbes at $4.5 billion, the sources said.