The program would be offered on a monthly basis and probably affect "only a few hundred pilots, at most," said Rick Dominguez, a spokesman for the Delta chapter of the Air Line Pilots Association.
Either side could terminate the arrangement.
Delta pilots usually fly between 12 and 19 days per month, depending on their plane, seniority and federal work rules.
The proposal has received mixed opinions among pilots, with some loathe to cut their salaries during a recession, but others keen on what would essentially be a paid holiday.
"They say, 'I have no responsibilities and I'll go spend a month in Fiji," Dominguez
said."There are 10,000 different opinions."
Atlanta-based Delta cut back its flight schedule by 16 percent after the attacks and has furloughed 400 pilots because of weak demand.Another 60 pilots are scheduled for furlough by the end of the January, with the company estimating it might lay off as many as 1,700 pilots if business continues to lag.
Delta shares fell 13 cents to $29.39 Wednesday afternoon on the New York Stock Exchange.