In the normal scheme of things I'd be telling you that there's no chance we could finish in the top 4 this year. We've finished 11th, 11th, 7th, 8th and 8th in the last 5 years.
Having said that, the main thing we have going in our favour is the turmoil of half of the top 6. City and Liverpool will be the top two. Spurs will most probably be third. Outside of that, Chelsea and United are a mess and Arsenal could go either way. There is a chance that the 4th place spot could be open for a non-top 6 side. I think it's probably less likely to happen than it is likely, but IF we have a really good window, it's possible. That would probably mean getting in all of our first choice targets in the 4 areas Silva wants and probably keeping Gana (even though I think longer term it might be smarter to sell him this summer).
It's a long shot, but it's theoretically possible. Will depend on at least 3 clubs having bad seasons though.