Asharq al-Awsat, a leading pan-Arab daily, has said al-Qaida has designated al-Migrin, 31, as the nominal leader of the group in Saudi Arabia because he is Saudi and this would help ensure the support of sympathisers in the country.
The newspaper did not give a source for its report, datelined Dammam in Saudi Arabia's Eastern Province.
Asharq al-Awsat noted al-Migrin topped the list of people wanted by authorities for presumed links with a series of suicide bombings that killed 52 people in Riyadh last year.
The list, originally of 26 names, has gone down to 23 since it was issued in December after the death of two militants and the surrender of a third.
While Hajj is a Yemeni national, he was born in the Saudi Red Sea city of Jidda.
The only Yemeni on the most-wanted list, he is in his thirties and goes by the name of Abu Hazim al-Shaair, Asharq al-Awsat said.
It said US intelligence reports in October spoke of signs that Hajj had become the operations commander of al-Qaida in the Gulf region, but the reports were not confirmed at the time.
Hajj is said to be in Riyadh, where he is being hunted by security forces, the paper added.
The interior ministry has warned residents of the Saudi capital a car rigged with explosives and registered to a wanted suspect could be used in an attack.