The investment group insisted it had not found anything during the due diligence programme which had caused it to abandon its interest in the club, and it was a decision made on purely economic grounds.
It also denied rumours it was considering a move for Everton and said it was in fact now not looking to invest in any English club.
"Contrary to recent press reports, Zabeel Investments has confirmed to Charlton that it has not approached any other club since it made an indicative offer for Charlton Athletic on 10 October, nor has it authorised any approach on its behalf," said the statement.
The news will be a big blow to the Addicks, who have reported debts of £20m.
The club are in the final year of their parachute payments following relegation from the Premier League in 2007, and after Tuesday's home loss to Bristol City they dropped to 20th in the table.
Charlton boss Alan Pardew told BBC Radio Five Live: "With the credit crisis the deal was always in danger.
"For us as a playing staff and management we have to move on quickly and discuss with the board how we can take the club forward."
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