Arab League Secretary-General Amr Moussa announced his intention to step down to run for president in Egypt. Moussa joins a list of candidates that includes diplomat and Nobel Peace Prize laureate Mohammed ElBaradei.
The Iraqi State of Law coalition said it proposed Allawi as the next head of the Arab League. Allawi, Maliki's top challenger in elections last year, backed out of a key strategic position amid a series of political flare-ups in Iraq.
Iraqiya leaders told the Voices of Iraq news agency they were honored by the nomination but had no discussion with Allawi on the matter.
Iraqiya lawmaker Zuhair al-Aarajy said his party wasn't officially informed of the nomination but noted Allawi "enjoys great respect" from several Arab leaders.
"All Iraqi political blocs hope that an Iraqi personality would hold the post of the Arab League's secretary-general," he added.
The Arab League during the weekend agreed that Baghdad would host its May 10 Arab summit.