Haitian officials involved in the investigation told the New York Times Mr Henry would currently be a suspect if he was not the head of government.
Mr Jaar also reportedly said he believed the intention of those responsible for the assassination had been to depose, rather than kill, the president and swear in a judge in his place.
Mr Jaar was reportedly detained in the Dominican Republic on Friday.
Phone calls between Mr Henry and Mr Badio were first disclosed in September by a Haitian prosecutor who was later fired.
A spokesman for Mr Henry said the prosecutor was fired for pursuing a political agenda.
Haiti’s Senate reconvened on Monday for the first time in a year as it prepares for elections following the assassination.
Mr Henry has pledged to hold general elections this year, but he has not provided a specific date.
The elections were originally scheduled for last year, but they were delayed by the pandemic, a spike in gang violence and the killing of Mr Moise.
Last week Mr Henry said he was targeted in an assassination attempt during recent national day celebrations.
He said: “An attempt has been made against me personally. My life has been put in the crosshairs.”
Photographs provided by Mr Henry’s office showed a bullet mark on the windshield of his armoured vehicle.