The others on the list, Iranian state media reported, were unnamed political and military officials from the U.S. and other countries that Tehran claimed had ties to the killing.
The US killed Soleimani, who oversaw the Revolutionary Guard's expeditionary Quds Force, and others in the January strike near Baghdad International Airport.
"It was possible to identify 36 persons who participated in preparations for and were involved in the assassination of Qasem Soleimani, among them political and military figures from the United States and other countries", Ali Alqasi-Mehr, Tehran's prosecutor-general, said in a statement on Monday.
Miffed by Soleimani's death, Iranian Revolutionary Guards vowed to attack Israel and other United States allies in revenge of USA action.
According to Alqasi-Mehr, Iran would pursue Trump's prosecution even after the expiry of his term as president.
The prosecutor was quoted as saying that Iran had requested a "red notice" be put out for Trump and the others, which represents the highest-level arrest request issued by Interpol. Tehran has requested the help of Interpol in securing their arrest.
Under a red notice, local authorities make the arrests on behalf of the country that requested it.
The assassination came after months of incidents raising tensions between the two countries and ultimately saw Iran retaliate with a ballistic missile strike targeting American troops in Iraq.