As far as patents (the topic of this site) are concerned, yes, there is a risk that reproducing that application will infringe on some patents. These patents may be held by the author of the application, or the author may have a license, or the author may be infringing. If you use different techniques inside to accomplish the same user-level behavior, the patents relevant to your application may be relevant from the ones relevant to the original.
There is no magic bullet to know whether your application might infringe on some patents, and you can't know before starting on your project since patents would cover implementation techniques: you'll need to do at least the design first. A professional patent search costs a significant amount of money.
On the upside, it's pretty unlikely that a smartphone app would involve patented techniques. Only you can decide whether to take the risk but the risk is low.
Off-topic: the code and artwork of the original app are covered by copyright. As long as you don't copy any of them, you won't infringe on the original app's copyright. The name of the app may be covered by a trade mark, which isn't a problem as long as you pick a sufficiently different name. The look and feel may or may not be covered by copyright: there isn't a clear jurisprudence on whether copying an interface wholesale (while using different graphics for the individual elements) is subject to legal restrictions. If you keep the same broad behavior while doing your own design for the details, your application is unlikely to be challenged on this grounds. The look and feel of a desktop app is likely to be pretty different from that of a mobile app anyway.