The offer with Spanish investment company Torreal SCR SA and publisher Groupo Planeta SA would keep 51 percent of Spain's largest airline by sales in Spanish hands, Pearson PLC's Expansion business newspaper in Madrid reported.
It would also let Iberia continue to fly certain routes in Spain and abroad, the newspaper said.
The bid -- whose dollar amount wasn't reported -- would seek to pre-empt a $4.8 billion preliminary offer being prepared by British Airways PLC.
British Airways is working with U.S. private-equity firm TPG Capital LP and Spanish firms Inversiones Ibersuizas SA, Vista Capital de Expansion SGECR SA and Quercus Equity SA.
Torreal is the investment vehicle of Juan Abello, a Spanish entrepreneur and former bank executive. Groupo Planeta is owned by Spain's wealthy Lara family, which controls low-cost carrier Vueling Airlines SA of Barcelona, Spain.
Iberia, whose profitability has been under pressure from easyJet PLC and Ryanair Holdings PLC after the low-fare airlines expanded operations in Spain, has been looking for a partner since at least March.
An Air France-KLM representative said it was "studying the dossier." Representatives of Iberia, Torreal, Planeta, British Airways and TPG had no immediate comment.