Chelsea and Arsenal will be the challengers for the second position because so far to catch Liverpool at the top of the standings is very difficult and if we talk about the title competition for Chelsea then I think it is beyond their ability at this time. Arsenal have always failed to dominate the league even though in the last few seasons their performance has been much more promising but if we talk about the title competition their ability is not so promising and always fails.
The race for a second position will be among three clubs, not only two, and in my opinion these clubs are Manchester City, Arsenal and Chelsea. They are most promissing clubs to finish this season in top four, and only one of them can end this season beyond top four but I see it's very unlikely to happen. Manchester City and Arsenal can secure their positions in top four and Chelsea have good improvement in this season, and I really don't believe other clubs can beat Chelsea in this race to top four.
For the second position, it's too early and many things can change so I think it's very soon for a prediction on this position.
Liverpool are much more stable this season and they have managed to perform consistently until now and I don't want to talk too much about the competition in the Champions League because even though they have a chance now, what needs to be thought about is how Liverpool can continue to be consistent in pursuing the English league title this season.
Liverpool if wont' suddenly have big problems with their star players, will be able to win Premier League title. Three big clubs mentioned above are not good and stable enough in this season, to beat Liverpool and become a new champion of this league. Chelsea looks to have good momentum but they will have to wait till a next season to compete for a title. Manchester City will need one or two seasons for Pep Guardiola to build up a third player generation to succeed again.