Yes, I think he does warrant another season, but as I have said on other threads, Klopp is a better option for me. I do believe the players Rodgers has signed are good, and suit his style of play, but I think we've missed 2/3 players from our line-up that turn the team into one able to finish highly. We need to improve on some options in the squad and sign a couple of top players, and I think he can do that...
But as I say. At this point in time, Klopp is the charismatic coach that has pulling power that Rodgers tries but fails at being right now. I think Rodgers may well go on to be a top manager at a top club, but right now, Liverpool need to make a decision for the clubs immediate future based on bringing the club and the fanbase together, and Klopp would do that. No other manager would in my view.