Both Papa Massata Diack and his 83-year-old father face charges in France over millions of dollars paid to cover up doping failures by Russian athletes.
Lamine Diack is barred from leaving France, while Papa Massata Diack has been in hiding in Dakar where Senegalese authorities have refused to extradite him.
Also implicated in possible corruption over the awarding of the 2016 Olympic Games to Rio, Papa Massata Diack has slammed the French investigation as a "witch hunt" against him.
"They should come to Senegal to investigate and I can respond formally instead of organising leaks in the press," he told AFP in an interview on Monday.
However, a French judicial source told AFP on Tuesday that in addition to the arrest warrant, a formal rogatory international letter was sent to Dakar in May 2016 calling for Papa Massata Diack's indictment.
"The Senegalese authorities have indicated that they will not execute this request," added the same source.
Meanwhile, former sprinter Frankie Fredericks quit as head of the IOC commission monitoring candidates for the 2024 Olympics on Tuesday amid a corruption probe.
Fredericks, 49, strongly denied any wrongdoing in accepting nearly $300,000 (283,000 euros) on the day that Rio de Janeiro was awarded the 2016 Olympics.
Le Monde newspaper on Friday said that Fredericks, a four-time Olympic silver medallist, received the sum from Papa Massata Diack's Pamodzi company on the day Rio won the right to host the 2016 Games.