Reuters was told of the plans by two sources.
The French-Dutch carrier hoped to raise just over $1.1 billion by the end of the year.
It wanted the cash to repay government aid and strengthen its heavily-indebted balance sheet, which was hit hard by the health crisis.
The sources said those targets will now likely be delayed.
It comes after a number of countries, including the U.S. and Japan, tightened borders due to the Omicron variant.
The airline completed a $4.5 billion recapitalisation package in April.
It included state support and a $1.1 billion rights issue which doubled the French government's stake to 30%.
But government bailouts have pushed Air France's total debt to $11.5 billion and borrowing costs have spiked over the last week.
Shares in travel companies have fallen sharply since the new variant was announced.
British Airways-owner IAG is down almost 15% since Friday.
Lufthansa and Air France-KLM are both down around 9%.
