Yes, liver problems could cause puffy eyes. There are many symptoms which could be caused by liver problems, yet there might be many reasons for eyes puffiness. Age could cause puffy eyes too, as the skin getting thinner and the skin is less elastic. If the puffiness is only apparent in the morning when you just get up, then relax, you are just witnessing how we sleep. Most of us have puffy eyes in the morning. If it is only a one day symptoms, you might drink too much water last night, yet if the puffy eyes that don't get less as the days go on could be sign that you body is fluid, which could be a symptom of serious kidney, heart or liver disease. A bad reaction to a new medication can also cause puffy eyes. It is hard to tell what exact problem causing your puffy eyes.
I suggest that you'd better have a detailed check especially if you also prone to puffy hands or ankles. Avoid drinking alcohol in the evening especially you suspect your liver to be compromised. Hope you could get well soon.