The plane was operated by GainJet, a charter company based in Greece that is often used by Kagame, the report said.
But it landed in Kigali where Rusesabagina was arrested. The NYT quoted Rwanda's spy chief as saying "he delivered himself here."
He has since been charged with terrorism, financing and founding militant groups, murder, arson and conspiracy to involve children in armed groups.
Rusesabagina says he was heading to Burundi at the invitation of a pastor, to speak in his churches.
But the NYT was not able to speak to the pastor, and says Rwandan officials believe he was actually heading there to coordinate with armed groups based in Burundi and Congo.
In 2018, Rusesabagina co-founded an opposition group, the Rwandan Movement for Democratic Change (MRCD), which is said to have an armed wing called the National Liberation Front (FLN).
In multiple speeches, Rusesabagina has expressed support for the FLN - which has carried out armed attacks and is described as a terrorist organisation by Rwanda -- but the extent of his involvement in its actions is unclear.
He has denied forming the FLN.