The reduction amounts to nearly 25 percent of the company's workforce of 20,000.
Iberia's parent company, International Airlines Group, which includes Iberia and British Airways, said Thursday it had made a $144 million bid for 54.5 percent of Spanish airline Vueling, ThinkSpain reported.
IAG already owns the other 45.5 percent, the report said.
The bid is being made to stem losses in Spain, where the economy is doing poorly.
The BBC reported that Iberia expects to trim its passenger capacity by 15 percent as it reduces its fleet from 156 to 131 planes.
IAG posted a profit of $429.8 million in the first nine months of 2011 but lost $49.5 million in the same period of 2012.