Ansa said four people who survived the shipwreck told rescuers they were on a boat carrying 45 people, including three children.
The boat set off on Thursday morning from Tunisia's Sfax, a hot spot in the migration crisis, but capsized and sank after a few hours, the survivors were quoted as saying.
The survivors - three men and a woman from Ivory Coast and Guinea - said they were rescued by a cargo ship and then transferred onto an Italian coast guard vessel.
The coast guard did not immediately respond to a request for comment.
It was unclear if the news given by Ansa was linked to the two shipwrecks the coast guard had reported on Sunday, saying about 30 people were missing from them.
The coast guard had also said it had recovered 57 survivors and two bodies, amid media reports at least one of the sunken boats had set off from Sfax on Thursday.
Separately, Tunisian authorities said on Monday they had recovered 11 bodies from a shipwreck near Sfax on Sunday, with 44 migrants still missing from that sinking.
Italy has recorded about 93,700 migrant arrivals by sea so far this year, according to interior ministry data last updated on Monday, compared to 44,700 in the same period last year.
