Eriksson met with representatives of the Iraq Football Association in Istanbul this week and a federation source said the Swede had agreed to take charge of the team.
The source said the matter would be discussed further by the federation on Monday.
Sources close to Eriksson, however, said the 70-year-old had yet to make a decision on whether to accept the offer.
Iraq are due to play in next year's Asian Cup finals, 12 years after claiming their sole continental title.
They have been drawn with Iran, Vietnam and Yemen in the group phase of the tournament, which will kick off in the United Arab Emirates on Jan. 5.
Eriksson, who led England to the quarter-finals of the 2002 World Cup finals, has not coached at international level since working with the Ivory Coast at the 2010 World Cup in South Africa.
His most recent role was in China's second division when he spent half a season with Shenzhen FC. He also had stints with Chinese Super League sides Guangzhou R&F and Shanghai SIPG.
Prior to working with England, Eriksson won league titles in Sweden, Portugal and Italy.
(Reporting by Michael Church, Editing by Peter Rutherford)
