But auction house Bonhams & Butterfields is in negotiations with a number of institutions and individuals, and Tom Lindgren, the company's natural history director, said he's confident a sale will be completed in the next couple of weeks.
The auctioneer had hoped bids would top $6 million for the T. rex dubbed "Samson." The highest bid at Saturday's auction at the Venetian hotel-casino was $3.7 million.
Lindgren said the owner had sought to sell the dinosaur as soon as possible, leaving potential bidders scrambling to quickly come up with the money.
"A number of bidders are still trying to get their financing in line," he said. "I think we'll have a home for her pretty soon."
Experts say the 170 fossilized bones discovered about 17 years ago in South Dakota represent more than half the skeleton of a 40-foot-long, 7.5-ton dinosaur that lived 66 million years ago.
A similar T. rex fossil sold for $8.3 million in 1997 and is now housed at the Field Museum in Chicago. That dinosaur, named "Sue," is 42 feet long and has more than 200 bones.
Lindgren said "Samson" is the third most complete T. rex skeleton ever discovered and has the "finest skull" of all T. rexes ever found.
The female dinosaur's lower jaw was found by the son of a rancher in 1987, and the rest of its bones were excavated in 1992, Lindgren said. It was sold twice to private owners and is now owned by an American whom Lindgren wouldn't name.
About 50 other lots fetched $1.76 million Saturday. World records included $458,000 for a duckbilled dinosaur, $440,000 for a pair of Einiosaurus skeletons and $422,000 for a 17-foot-long fossilized fish found in Kansas, Lindgren said.
"This was the most successful auction we've ever had," he said.