Not generally "offered" but, your best chance to meet the engineer might be at the start or end of the run. You would need to be on the platform when the engineer boards or leaves the locomotive. If its a long distance train, a crew change point might be a possibility.
It will all depend on the personality/mood of the engineer and if he/she is willing to take the time. There will not be an opportunity to get in the cab.
Its a long shot but, you never know until you try.. Good luck!