It would have to turn to private equity or extend its credit line of $750 million to come up with the money for an all-cash bid.
Cnooc made its higher, all-cash bid on June 23.
The company also offered an all-cash alternative bid of 915 pence a share, or about $:1.01 billion.
Minmetals announced its intention to make an all-cash bid for Noranda last month.
The last-minute all-cash bid from Eni underscores the urgency among energy companies to increase production through consolidation.
The company added that it was prepared to make an all-cash bid if Damon established a fair-bidding process.
The all-cash bid was for $60.50 a share, an 11 percent premium to the previous day's stock price.
Regulators said that Columbia executives had failed to get the highest value for the portfolio because they had not sought any all-cash bids.
Thanks to the company's cash trove, totaling some $10.5 billion, an all-cash bid was no problem.
Daystar sued in state court, stating that under the terms of the auction, its all-cash bid should have been accepted.