What you need here is a little Market Research.
It sounds like there are no technological factors that would bind you to building an app - you don't need to use any of the device's specialist hardware to complete your processes.
At the same time there's nothing really to stop you from building the functionality from your website into an app.
This is the point where you need to ask your users what they would prefer. You could ask them questions like "How important is it for you to be able to use this service without an internet connection?", "What do you use the service for?", "How often do you use the service?", "Where are you when you use the service most?", etc.
Focus on finding questions that relate to the advantages and disadvantages of using we-based and app-based versions of your service. If you choose your questions carefully, you should be able to gauge the value of developing an app from the answers you get without actually asking "Do you want this in an app?".