I was under the impression that they were flying on a privately owned plane. That does not seem to be the case, but it may be on their next leg of the journey.

I do not have direct knowledge, but I would think that if the plane is of the diplomat, then the whole plane could be considered to be territory of the nation of the diplomat, therefore the diplomat could offer him asylum while on the plane.

If I wasn't clear, I was not speaking about offering him diplomatic immunity, but rather the plane being considered as territory of the nation of the diplomat.