Riyadh cut ties with Tehran in January after Iranian demonstrators torched its embassy.
The Al-Hayat daily reported that Riyadh's pilgrims minister Mohammed Bentin had opened discussions with more than 80 countries, including Iran, to work out the details of the 2017 hajj.
"Iran's hajj delegation was invited to come to the kingdom" for preparations, the paper said.
The Arab News daily said Riyadh would welcome pilgrims for hajj and the smaller umra rite "irrespective of their nationalities or sectarian affiliations, including Iranian pilgrims".
More than 1.8 million faithful took part in this year's hajj, but Iranians stayed at home after tensions between Riyadh and Tehran boiled over following a deadly stampede during the 2015 pilgrimage.
Iran says it lost 464 people in the crush outside Mecca.
They were among more than 2,300 people killed in the worst ever disaster to strike the hajj -- one of the five pillars of Islam -- which capable Muslims must perform at least once.
Shiite Iran and predominantly Sunni Saudi Arabia are at odds over a raft of regional issues, notably the conflicts in Syria and Yemen in which they support opposing sides.
Riyadh cut ties with Tehran in January after Iranian demonstrators torched its embassy and a consulate following its execution of a prominent Shiite cleric.